LMFDB - Embedded newform 520.2.ca.a.101.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.26
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.26

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28986 - 0.579890i) q^{2} +(1.05921 - 0.611534i) q^{3} +(1.32746 - 1.49595i) q^{4} -1.00000 q^{5} +(1.01160 - 1.40301i) q^{6} +(3.94053 + 2.27507i) q^{7} +(0.844743 - 2.69934i) q^{8} +(-0.752053 + 1.30259i) q^{9} +(-1.28986 + 0.579890i) q^{10} +(-0.572114 - 0.990930i) q^{11} +(0.491229 - 2.39630i) q^{12} +(0.184836 - 3.60081i) q^{13} +(6.40201 + 0.649436i) q^{14} +(-1.05921 + 0.611534i) q^{15} +(-0.475720 - 3.97161i) q^{16} +(0.505178 - 0.874994i) q^{17} +(-0.214679 + 2.11626i) q^{18} +(-2.97393 + 5.15100i) q^{19} +(-1.32746 + 1.49595i) q^{20} +5.56512 q^{21} +(-1.31257 - 0.946395i) q^{22} +(-0.586182 - 1.01530i) q^{23} +(-0.755977 - 3.37575i) q^{24} +1.00000 q^{25} +(-1.84966 - 4.75171i) q^{26} +5.50883i q^{27} +(8.63427 - 2.87478i) q^{28} +(-3.04627 + 1.75877i) q^{29} +(-1.01160 + 1.40301i) q^{30} -0.814108i q^{31} +(-2.91670 - 4.84694i) q^{32} +(-1.21198 - 0.699734i) q^{33} +(0.144207 - 1.42156i) q^{34} +(-3.94053 - 2.27507i) q^{35} +(0.950295 + 2.85417i) q^{36} +(-3.97121 - 6.87834i) q^{37} +(-0.848931 + 8.36860i) q^{38} +(-2.00624 - 3.92704i) q^{39} +(-0.844743 + 2.69934i) q^{40} +(-7.63515 + 4.40815i) q^{41} +(7.17821 - 3.22716i) q^{42} +(-1.17648 - 0.679243i) q^{43} +(-2.24184 - 0.459564i) q^{44} +(0.752053 - 1.30259i) q^{45} +(-1.34485 - 0.969666i) q^{46} -9.05737i q^{47} +(-2.93266 - 3.91584i) q^{48} +(6.85187 + 11.8678i) q^{49} +(1.28986 - 0.579890i) q^{50} -1.23573i q^{51} +(-5.14126 - 5.05642i) q^{52} +8.10029i q^{53} +(3.19451 + 7.10559i) q^{54} +(0.572114 + 0.990930i) q^{55} +(9.46991 - 8.71497i) q^{56} +7.27464i q^{57} +(-2.90936 + 4.03506i) q^{58} +(3.14969 - 5.45542i) q^{59} +(-0.491229 + 2.39630i) q^{60} +(10.5468 + 6.08920i) q^{61} +(-0.472093 - 1.05008i) q^{62} +(-5.92698 + 3.42194i) q^{63} +(-6.57282 - 4.56049i) q^{64} +(-0.184836 + 3.60081i) q^{65} +(-1.96904 - 0.199745i) q^{66} +(5.23119 + 9.06069i) q^{67} +(-0.638344 - 1.91724i) q^{68} +(-1.24178 - 0.716940i) q^{69} +(-6.40201 - 0.649436i) q^{70} +(-5.04169 - 2.91082i) q^{71} +(2.88084 + 3.13040i) q^{72} +14.5790i q^{73} +(-9.11096 - 6.56920i) q^{74} +(1.05921 - 0.611534i) q^{75} +(3.75786 + 11.2866i) q^{76} -5.20639i q^{77} +(-4.86501 - 3.90192i) q^{78} -5.60175 q^{79} +(0.475720 + 3.97161i) q^{80} +(1.11268 + 1.92721i) q^{81} +(-7.29200 + 10.1134i) q^{82} +2.31651 q^{83} +(7.38746 - 8.32514i) q^{84} +(-0.505178 + 0.874994i) q^{85} +(-1.91138 - 0.193895i) q^{86} +(-2.15109 + 3.72580i) q^{87} +(-3.15814 + 0.707246i) q^{88} +(-12.1107 + 6.99213i) q^{89} +(0.214679 - 2.11626i) q^{90} +(8.92044 - 13.7686i) q^{91} +(-2.29696 - 0.470865i) q^{92} +(-0.497854 - 0.862309i) q^{93} +(-5.25227 - 11.6827i) q^{94} +(2.97393 - 5.15100i) q^{95} +(-6.05347 - 3.35025i) q^{96} +(4.36544 + 2.52039i) q^{97} +(15.7199 + 11.3344i) q^{98} +1.72104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.28986	−	0.579890i	0.912066	−	0.410044i
$2$	1.28986	−	0.579890i	0.912066	−	0.410044i
$3$	1.05921	−	0.611534i	0.611534	−	0.353069i	−0.162032	−	0.986786i	$-0.551805\pi$
$3$	1.05921	−	0.611534i	0.611534	−	0.353069i	0.773566	+	0.633716i	$0.218471\pi$
$4$	1.32746	−	1.49595i	0.663728	−	0.747974i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.01160	−	1.40301i	0.412985	−	0.572778i
$7$	3.94053	+	2.27507i	1.48938	+	0.859895i	0.999926	−	0.0121337i	$-0.00386237\pi$
$7$	3.94053	+	2.27507i	1.48938	+	0.859895i	0.489455	+	0.872029i	$0.337196\pi$
$8$	0.844743	−	2.69934i	0.298662	−	0.954359i
$9$	−0.752053	+	1.30259i	−0.250684	+	0.434198i
$10$	−1.28986	+	0.579890i	−0.407888	+	0.183377i
$11$	−0.572114	−	0.990930i	−0.172499	−	0.298777i	0.766794	−	0.641893i	$-0.221851\pi$
$11$	−0.572114	−	0.990930i	−0.172499	−	0.298777i	−0.939293	+	0.343116i	$0.888517\pi$
$12$	0.491229	−	2.39630i	0.141806	−	0.691753i
$13$	0.184836	−	3.60081i	0.0512643	−	0.998685i
$13$	0.184836	−	3.60081i	0.0512643	−	0.998685i
$14$	6.40201	+	0.649436i	1.71101	+	0.173569i
$15$	−1.05921	+	0.611534i	−0.273486	+	0.157897i
$16$	−0.475720	−	3.97161i	−0.118930	−	0.992903i
$17$	0.505178	−	0.874994i	0.122524	−	0.212217i	−0.798239	−	0.602341i	$-0.794235\pi$
$17$	0.505178	−	0.874994i	0.122524	−	0.212217i	0.920762	+	0.390124i	$0.127568\pi$
$18$	−0.214679	+	2.11626i	−0.0506004	+	0.498808i
$19$	−2.97393	+	5.15100i	−0.682266	+	1.18172i	0.292021	+	0.956412i	$0.405672\pi$
$19$	−2.97393	+	5.15100i	−0.682266	+	1.18172i	−0.974288	+	0.225308i	$0.927661\pi$
$20$	−1.32746	+	1.49595i	−0.296828	+	0.334504i
$21$	5.56512			1.21441
$22$	−1.31257	−	0.946395i	−0.279842	−	0.201772i
$23$	−0.586182	−	1.01530i	−0.122227	−	0.211704i	0.798418	−	0.602103i	$-0.205670\pi$
$23$	−0.586182	−	1.01530i	−0.122227	−	0.211704i	−0.920646	+	0.390399i	$0.872337\pi$
$24$	−0.755977	−	3.37575i	−0.154313	−	0.689071i
$25$	1.00000			0.200000
$26$	−1.84966	−	4.75171i	−0.362748	−	0.931887i
$27$			5.50883i			1.06017i
$28$	8.63427	−	2.87478i	1.63172	−	0.543282i
$29$	−3.04627	+	1.75877i	−0.565679	+	0.326595i	−0.755422	−	0.655239i	$-0.772568\pi$
$29$	−3.04627	+	1.75877i	−0.565679	+	0.326595i	0.189743	+	0.981834i	$0.439235\pi$
$30$	−1.01160	+	1.40301i	−0.184693	+	0.256154i
$31$		−	0.814108i		−	0.146218i	−0.997324	−	0.0731090i	$-0.976708\pi$
$31$		−	0.814108i		−	0.146218i	0.997324	−	0.0731090i	$-0.0232921\pi$
$32$	−2.91670	−	4.84694i	−0.515605	−	0.856826i
$33$	−1.21198	−	0.699734i	−0.210978	−	0.121808i
$34$	0.144207	−	1.42156i	0.0247313	−	0.243796i
$35$	−3.94053	−	2.27507i	−0.666072	−	0.384557i
$36$	0.950295	+	2.85417i	0.158382	+	0.475694i
$37$	−3.97121	−	6.87834i	−0.652863	−	1.13079i	−0.982425	−	0.186658i	$-0.940234\pi$
$37$	−3.97121	−	6.87834i	−0.652863	−	1.13079i	0.329562	−	0.944134i	$-0.393099\pi$
$38$	−0.848931	+	8.36860i	−0.137715	+	1.35757i
$39$	−2.00624	−	3.92704i	−0.321255	−	0.628830i
$40$	−0.844743	+	2.69934i	−0.133566	+	0.426802i
$41$	−7.63515	+	4.40815i	−1.19241	+	0.688438i	−0.958852	−	0.283905i	$-0.908370\pi$
$41$	−7.63515	+	4.40815i	−1.19241	+	0.688438i	−0.233557	+	0.972343i	$0.575037\pi$
$42$	7.17821	−	3.22716i	1.10762	−	0.497961i
$43$	−1.17648	−	0.679243i	−0.179412	−	0.103584i	0.407604	−	0.913159i	$-0.366364\pi$
$43$	−1.17648	−	0.679243i	−0.179412	−	0.103584i	−0.587016	+	0.809575i	$0.699698\pi$
$44$	−2.24184	−	0.459564i	−0.337970	−	0.0692819i
$45$	0.752053	−	1.30259i	0.112109	−	0.194179i
$46$	−1.34485	−	0.969666i	−0.198287	−	0.142969i
$47$		−	9.05737i		−	1.32115i	−0.750759	−	0.660576i	$-0.770312\pi$
$47$		−	9.05737i		−	1.32115i	0.750759	−	0.660576i	$-0.229688\pi$
$48$	−2.93266	−	3.91584i	−0.423293	−	0.565203i
$49$	6.85187	+	11.8678i	0.978838	+	1.69540i
$50$	1.28986	−	0.579890i	0.182413	−	0.0820088i
$51$		−	1.23573i		−	0.173037i
$52$	−5.14126	−	5.05642i	−0.712965	−	0.701200i
$53$			8.10029i			1.11266i	0.830961	+	0.556330i	$0.187791\pi$
$53$			8.10029i			1.11266i	−0.830961	+	0.556330i	$0.812209\pi$
$54$	3.19451	+	7.10559i	0.434718	+	0.966949i
$55$	0.572114	+	0.990930i	0.0771438	+	0.133617i
$56$	9.46991	−	8.71497i	1.26547	−	1.16459i
$57$			7.27464i			0.963549i
$58$	−2.90936	+	4.03506i	−0.382018	+	0.529829i
$59$	3.14969	−	5.45542i	0.410055	−	0.710235i	−0.584841	−	0.811148i	$-0.698843\pi$
$59$	3.14969	−	5.45542i	0.410055	−	0.710235i	0.994895	+	0.100913i	$0.0321763\pi$
$60$	−0.491229	+	2.39630i	−0.0634174	+	0.309362i
$61$	10.5468	+	6.08920i	1.35038	+	0.779643i	0.988303	−	0.152505i	$-0.0487341\pi$
$61$	10.5468	+	6.08920i	1.35038	+	0.779643i	0.362078	+	0.932148i	$0.382067\pi$
$62$	−0.472093	−	1.05008i	−0.0599558	−	0.133360i
$63$	−5.92698	+	3.42194i	−0.746729	+	0.431124i
$64$	−6.57282	−	4.56049i	−0.821602	−	0.570061i
$65$	−0.184836	+	3.60081i	−0.0229261	+	0.446626i
$66$	−1.96904	−	0.199745i	−0.242372	−	0.0245869i
$67$	5.23119	+	9.06069i	0.639092	+	1.10694i	0.985632	+	0.168905i	$0.0540230\pi$
$67$	5.23119	+	9.06069i	0.639092	+	1.10694i	−0.346540	+	0.938035i	$0.612644\pi$
$68$	−0.638344	−	1.91724i	−0.0774105	−	0.232499i
$69$	−1.24178	−	0.716940i	−0.149492	−	0.0863094i
$70$	−6.40201	−	0.649436i	−0.765186	−	0.0776224i
$71$	−5.04169	−	2.91082i	−0.598339	−	0.345451i	0.170049	−	0.985436i	$-0.445607\pi$
$71$	−5.04169	−	2.91082i	−0.598339	−	0.345451i	−0.768388	+	0.639985i	$0.778941\pi$
$72$	2.88084	+	3.13040i	0.339511	+	0.368921i
$73$			14.5790i			1.70635i	0.521628	+	0.853173i	$0.325325\pi$
$73$			14.5790i			1.70635i	−0.521628	+	0.853173i	$0.674675\pi$
$74$	−9.11096	−	6.56920i	−1.05913	−	0.763654i
$75$	1.05921	−	0.611534i	0.122307	−	0.0706139i
$76$	3.75786	+	11.2866i	0.431056	+	1.29466i
$77$		−	5.20639i		−	0.593323i
$78$	−4.86501	−	3.90192i	−0.550854	−	0.441805i
$79$	−5.60175			−0.630246			−0.315123	−	0.949051i	$-0.602046\pi$
$79$	−5.60175			−0.630246			−0.315123	+	0.949051i	$0.602046\pi$
$80$	0.475720	+	3.97161i	0.0531871	+	0.444040i
$81$	1.11268	+	1.92721i	0.123631	+	0.214135i
$82$	−7.29200	+	10.1134i	−0.805266	+	1.11684i
$83$	2.31651			0.254270			0.127135	−	0.991885i	$-0.459422\pi$
$83$	2.31651			0.254270			0.127135	+	0.991885i	$0.459422\pi$
$84$	7.38746	−	8.32514i	0.806038	−	0.908347i
$85$	−0.505178	+	0.874994i	−0.0547943	+	0.0949064i
$86$	−1.91138	−	0.193895i	−0.206109	−	0.0209082i
$87$	−2.15109	+	3.72580i	−0.230621	+	0.399448i
$88$	−3.15814	+	0.707246i	−0.336659	+	0.0753927i
$89$	−12.1107	+	6.99213i	−1.28373	+	0.741164i	−0.977529	−	0.210802i	$-0.932393\pi$
$89$	−12.1107	+	6.99213i	−1.28373	+	0.741164i	−0.306205	+	0.951966i	$0.599059\pi$
$90$	0.214679	−	2.11626i	0.0226292	−	0.223074i
$91$	8.92044	−	13.7686i	0.935116	−	1.44334i
$92$	−2.29696	−	0.470865i	−0.239475	−	0.0490910i
$93$	−0.497854	−	0.862309i	−0.0516251	−	0.0894173i
$94$	−5.25227	−	11.6827i	−0.541730	−	1.20498i
$95$	2.97393	−	5.15100i	0.305119	−	0.528481i
$96$	−6.05347	−	3.35025i	−0.617829	−	0.341934i
$97$	4.36544	+	2.52039i	0.443243	+	0.255906i	0.704972	−	0.709235i	$-0.250959\pi$
$97$	4.36544	+	2.52039i	0.443243	+	0.255906i	−0.261729	+	0.965141i	$0.584293\pi$
$98$	15.7199	+	11.3344i	1.58795	+	1.14495i
$99$	1.72104			0.172971
$100$	1.32746	−	1.49595i	0.132746	−	0.149595i
$101$	6.95428	−	4.01506i	0.691977	−	0.399513i	−0.112375	−	0.993666i	$-0.535846\pi$
$101$	6.95428	−	4.01506i	0.691977	−	0.399513i	0.804352	+	0.594153i	$0.202513\pi$
$102$	−0.716589	−	1.59392i	−0.0709529	−	0.157821i
$103$	6.09755			0.600809			0.300405	−	0.953812i	$-0.402878\pi$
$103$	6.09755			0.600809			0.300405	+	0.953812i	$0.402878\pi$
$104$	−9.56365	−	3.54069i	−0.937793	−	0.347194i
$105$	−5.56512			−0.543101
$106$	4.69727	+	10.4482i	0.456239	+	1.01482i
$107$	−8.69066	+	5.01756i	−0.840158	+	0.485065i	−0.857318	−	0.514787i	$-0.827871\pi$
$107$	−8.69066	+	5.01756i	−0.840158	+	0.485065i	0.0171600	+	0.999853i	$0.494538\pi$
$108$	8.24092	+	7.31273i	0.792983	+	0.703667i
$109$	8.28364			0.793429			0.396714	−	0.917942i	$-0.370150\pi$
$109$	8.28364			0.793429			0.396714	+	0.917942i	$0.370150\pi$
$110$	1.31257	+	0.946395i	0.125149	+	0.0902352i
$111$	−8.41267	−	4.85706i	−0.798495	−	0.461012i
$112$	7.16109	−	16.7326i	0.676660	−	1.58108i
$113$	5.45926	−	9.45571i	0.513564	−	0.889519i	−0.486312	−	0.873785i	$-0.661658\pi$
$113$	5.45926	−	9.45571i	0.513564	−	0.889519i	0.999876	−	0.0157336i	$-0.00500837\pi$
$114$	4.21849	+	9.38323i	0.395097	+	0.878820i
$115$	0.586182	+	1.01530i	0.0546617	+	0.0946769i
$116$	−1.41277	+	6.89175i	−0.131173	+	0.639883i
$117$	4.55138	+	2.94876i	0.420776	+	0.272613i
$118$	0.899103	−	8.86318i	0.0827692	−	0.815922i
$119$	3.98134	−	2.29863i	0.364969	−	0.210715i
$120$	0.755977	+	3.37575i	0.0690109	+	0.308162i
$121$	4.84537	−	8.39243i	0.440488	−	0.762948i
$122$	17.1349	+	1.73821i	1.55132	+	0.157370i
$123$	−5.39147	+	9.33830i	−0.486133	+	0.842006i
$124$	−1.21786	−	1.08069i	−0.109367	−	0.0970490i
$125$	−1.00000			−0.0894427
$126$	−5.66060	+	7.85080i	−0.504286	+	0.699405i
$127$	−4.34447	−	7.52484i	−0.385509	−	0.667722i	0.606330	−	0.795213i	$-0.292641\pi$
$127$	−4.34447	−	7.52484i	−0.385509	−	0.667722i	−0.991840	+	0.127491i	$0.959308\pi$
$128$	−11.1226	−	2.07086i	−0.983105	−	0.183040i
$129$	−1.66152			−0.146289
$130$	1.84966	+	4.75171i	0.162226	+	0.416753i
$131$		−	18.5123i		−	1.61743i	−0.588201	−	0.808715i	$-0.700164\pi$
$131$		−	18.5123i		−	1.61743i	0.588201	−	0.808715i	$-0.299836\pi$
$132$	−2.65561	+	0.884185i	−0.231141	+	0.0769584i
$133$	−23.4377	+	13.5318i	−2.03231	+	1.17335i
$134$	12.0017	+	8.65347i	1.03679	+	0.747546i
$135$		−	5.50883i		−	0.474124i
$136$	−1.93516	−	2.10279i	−0.165938	−	0.180313i
$137$	−1.42212	−	0.821060i	−0.121500	−	0.0701479i	0.438018	−	0.898966i	$-0.355680\pi$
$137$	−1.42212	−	0.821060i	−0.121500	−	0.0701479i	−0.559518	+	0.828818i	$0.689014\pi$
$138$	−2.01746	−	0.204656i	−0.171738	−	0.0174215i
$139$	−14.6180	−	8.43972i	−1.23988	−	0.715848i	−0.270814	−	0.962632i	$-0.587293\pi$
$139$	−14.6180	−	8.43972i	−1.23988	−	0.715848i	−0.969070	+	0.246784i	$0.920626\pi$
$140$	−8.63427	+	2.87478i	−0.729729	+	0.242963i
$141$	−5.53889	−	9.59363i	−0.466458	−	0.807930i
$142$	−8.19101	−	0.830917i	−0.687375	−	0.0697290i
$143$	−3.67390	+	1.87691i	−0.307227	+	0.156955i
$144$	5.53116	+	2.36719i	0.460930	+	0.197266i
$145$	3.04627	−	1.75877i	0.252979	−	0.146058i
$146$	8.45422	+	18.8048i	0.699677	+	1.55630i
$147$	14.5151	+	8.38030i	1.19719	+	0.691195i
$148$	−15.5612	−	3.18997i	−1.27913	−	0.262214i
$149$	−7.39536	+	12.8091i	−0.605852	+	1.04937i	0.386065	+	0.922472i	$0.373834\pi$
$149$	−7.39536	+	12.8091i	−0.605852	+	1.04937i	−0.991916	+	0.126894i	$0.959499\pi$
$150$	1.01160	−	1.40301i	0.0825971	−	0.114556i
$151$			7.24626i			0.589692i	0.955545	+	0.294846i	$0.0952683\pi$
$151$			7.24626i			0.589692i	−0.955545	+	0.294846i	$0.904732\pi$
$152$	11.3921	+	12.3789i	0.924018	+	1.00406i
$153$	0.759841	+	1.31608i	0.0614295	+	0.106399i
$154$	−3.01913	−	6.71550i	−0.243289	−	0.541150i
$155$			0.814108i			0.0653907i
$156$	−8.53784	−	2.21175i	−0.683574	−	0.177081i
$157$			8.00548i			0.638907i	0.947602	+	0.319453i	$0.103499\pi$
$157$			8.00548i			0.638907i	−0.947602	+	0.319453i	$0.896501\pi$
$158$	−7.22545	+	3.24840i	−0.574826	+	0.258429i
$159$	4.95360	+	8.57989i	0.392846	+	0.680430i
$160$	2.91670	+	4.84694i	0.230586	+	0.383184i
$161$		−	5.33441i		−	0.420411i
$162$	2.55276	+	1.84060i	0.200564	+	0.144611i
$163$	−1.57351	+	2.72541i	−0.123247	+	0.213470i	−0.921046	−	0.389453i	$-0.872664\pi$
$163$	−1.57351	+	2.72541i	−0.123247	+	0.213470i	0.797799	+	0.602923i	$0.205997\pi$
$164$	−3.54096	+	17.2734i	−0.276502	+	1.34883i
$165$	1.21198	+	0.699734i	0.0943521	+	0.0544742i
$166$	2.98796	−	1.34332i	0.231911	−	0.104262i
$167$	9.82233	−	5.67093i	0.760075	−	0.438829i	−0.0692478	−	0.997599i	$-0.522060\pi$
$167$	9.82233	−	5.67093i	0.760075	−	0.438829i	0.829323	+	0.558770i	$0.188727\pi$
$168$	4.70110	−	15.0221i	0.362698	−	1.15898i
$169$	−12.9317	−	1.33112i	−0.994744	−	0.102394i
$170$	−0.144207	+	1.42156i	−0.0110602	+	0.109029i
$171$	−4.47310	−	7.74764i	−0.342067	−	0.592477i
$172$	−2.57784	+	0.858292i	−0.196559	+	0.0654442i
$173$	17.0348	+	9.83505i	1.29513	+	0.747745i	0.979559	−	0.201157i	$-0.0644701\pi$
$173$	17.0348	+	9.83505i	1.29513	+	0.747745i	0.315573	+	0.948901i	$0.397803\pi$
$174$	−0.614046	+	6.05314i	−0.0465507	+	0.458887i
$175$	3.94053	+	2.27507i	0.297876	+	0.171979i
$176$	−3.66342	+	2.74362i	−0.276141	+	0.206808i
$177$		−	7.70457i		−	0.579111i
$178$	−11.5664	+	16.0417i	−0.866940	+	1.20238i
$179$	2.69851	−	1.55798i	0.201696	−	0.116449i	−0.395750	−	0.918358i	$-0.629515\pi$
$179$	2.69851	−	1.55798i	0.201696	−	0.116449i	0.597446	+	0.801909i	$0.296182\pi$
$180$	−0.950295	−	2.85417i	−0.0708308	−	0.212737i
$181$		−	24.7399i		−	1.83891i	−0.393200	−	0.919453i	$-0.628632\pi$
$181$		−	24.7399i		−	1.83891i	0.393200	−	0.919453i	$-0.371368\pi$
$182$	3.52182	−	22.9324i	0.261054	−	1.69986i
$183$	14.8950			1.10107
$184$	−3.23580	+	0.724636i	−0.238546	+	0.0534209i
$185$	3.97121	+	6.87834i	0.291969	+	0.505705i
$186$	−1.14220	−	0.823554i	−0.0837505	−	0.0603859i
$187$	−1.15608			−0.0845408
$188$	−13.5493	−	12.0233i	−0.988188	−	0.876886i
$189$	−12.5330	+	21.7077i	−0.911638	+	1.57900i
$190$	0.848931	−	8.36860i	0.0615880	−	0.607122i
$191$	1.36233	−	2.35962i	0.0985744	−	0.170736i	−0.812520	−	0.582933i	$-0.801905\pi$
$191$	1.36233	−	2.35962i	0.0985744	−	0.170736i	0.911095	+	0.412197i	$0.135238\pi$
$192$	−9.75087	−	0.811003i	−0.703709	−	0.0585291i
$193$	3.88542	−	2.24325i	0.279679	−	0.161472i	−0.353599	−	0.935397i	$-0.615042\pi$
$193$	3.88542	−	2.24325i	0.279679	−	0.161472i	0.633278	+	0.773924i	$0.281709\pi$
$194$	7.09233	+	0.719464i	0.509200	+	0.0516545i
$195$	2.00624	+	3.92704i	0.143670	+	0.281221i
$196$	26.8491	+	5.50393i	1.91780	+	0.393138i
$197$	−11.1395	−	19.2942i	−0.793658	−	1.37466i	−0.923688	−	0.383146i	$-0.874841\pi$
$197$	−11.1395	−	19.2942i	−0.793658	−	1.37466i	0.130029	−	0.991510i	$-0.458493\pi$
$198$	2.21989	−	0.998012i	0.157761	−	0.0709257i
$199$	11.7148	−	20.2907i	0.830443	−	1.43837i	−0.0672446	−	0.997737i	$-0.521421\pi$
$199$	11.7148	−	20.2907i	0.830443	−	1.43837i	0.897687	−	0.440633i	$-0.145246\pi$
$200$	0.844743	−	2.69934i	0.0597323	−	0.190872i
$201$	11.0818	+	6.39810i	0.781653	+	0.451287i
$202$	6.64173	−	9.21156i	0.467311	−	0.648123i
$203$	−16.0053			−1.12335
$204$	−1.84859	−	1.64038i	−0.129427	−	0.114850i
$205$	7.63515	−	4.40815i	0.533262	−	0.307879i
$206$	7.86496	−	3.53590i	0.547978	−	0.246358i
$207$	1.76336			0.122562
$208$	−14.3889	+	0.978879i	−0.997694	+	0.0678730i
$209$	6.80571			0.470761
$210$	−7.17821	+	3.22716i	−0.495343	+	0.222695i
$211$	10.7239	−	6.19145i	0.738264	−	0.426237i	−0.0831739	−	0.996535i	$-0.526506\pi$
$211$	10.7239	−	6.19145i	0.738264	−	0.426237i	0.821438	+	0.570298i	$0.193172\pi$
$212$	12.1176	+	10.7528i	0.832241	+	0.738504i
$213$	−7.12027			−0.487873
$214$	−8.30007	+	11.5115i	−0.567381	+	0.786913i
$215$	1.17648	+	0.679243i	0.0802355	+	0.0463240i
$216$	14.8702	+	4.65354i	1.01179	+	0.316633i
$217$	1.85215	−	3.20802i	0.125732	−	0.217774i
$218$	10.6847	−	4.80359i	0.723659	−	0.325340i
$219$	8.91557	+	15.4422i	0.602458	+	1.04349i
$220$	2.24184	+	0.459564i	0.151145	+	0.0309838i
$221$	−3.05731	−	1.98078i	−0.205657	−	0.133242i
$222$	−13.6677	−	1.38649i	−0.917315	−	0.0930548i
$223$	−19.5063	+	11.2620i	−1.30624	+	0.754159i	−0.981467	−	0.191632i	$-0.938622\pi$
$223$	−19.5063	+	11.2620i	−1.30624	+	0.754159i	−0.324775	+	0.945791i	$0.605289\pi$
$224$	−0.466254	−	25.7352i	−0.0311529	−	1.71951i
$225$	−0.752053	+	1.30259i	−0.0501368	+	0.0868395i
$226$	1.55839	−	15.3623i	0.103662	−	1.02188i
$227$	−8.13510	+	14.0904i	−0.539946	+	0.935214i	0.458960	+	0.888457i	$0.348222\pi$
$227$	−8.13510	+	14.0904i	−0.539946	+	0.935214i	−0.998906	+	0.0467570i	$0.985111\pi$
$228$	10.8825	+	9.65676i	0.720710	+	0.639535i
$229$	5.90333			0.390103			0.195051	−	0.980793i	$-0.437513\pi$
$229$	5.90333			0.390103			0.195051	+	0.980793i	$0.437513\pi$
$230$	1.34485	+	0.969666i	0.0886768	+	0.0639379i
$231$	−3.18389	−	5.51465i	−0.209484	−	0.362837i
$232$	2.17418	+	9.70862i	0.142742	+	0.637402i
$233$	−0.205797			−0.0134822			−0.00674110	−	0.999977i	$-0.502146\pi$
$233$	−0.205797			−0.0134822			−0.00674110	+	0.999977i	$0.502146\pi$
$234$	7.58059	+	1.16418i	0.495559	+	0.0761049i
$235$			9.05737i			0.590837i
$236$	−3.97995	−	11.9536i	−0.259073	−	0.778113i
$237$	−5.93342	+	3.42566i	−0.385417	+	0.222521i
$238$	3.80241	−	5.27364i	0.246473	−	0.341839i
$239$		−	22.3457i		−	1.44542i	−0.691150	−	0.722711i	$-0.742896\pi$
$239$		−	22.3457i		−	1.44542i	0.691150	−	0.722711i	$-0.257104\pi$
$240$	2.93266	+	3.91584i	0.189302	+	0.252767i
$241$	−5.21726	−	3.01218i	−0.336073	−	0.194032i	0.322461	−	0.946583i	$-0.395490\pi$
$241$	−5.21726	−	3.01218i	−0.336073	−	0.194032i	−0.658534	+	0.752551i	$0.728823\pi$
$242$	1.38315	−	13.6348i	0.0889122	−	0.876478i
$243$	−11.9552	−	6.90236i	−0.766929	−	0.442787i
$244$	23.1096	−	7.69432i	1.47944	−	0.492579i
$245$	−6.85187	−	11.8678i	−0.437750	−	0.758205i
$246$	−1.53904	+	15.1715i	−0.0981254	+	0.967301i
$247$	17.9981	+	11.6606i	1.14519	+	0.741949i
$248$	−2.19755	−	0.687712i	−0.139545	−	0.0436697i
$249$	2.45366	−	1.41662i	0.155495	−	0.0897749i
$250$	−1.28986	+	0.579890i	−0.0815776	+	0.0366754i
$251$	18.0416	+	10.4163i	1.13878	+	0.657472i	0.946127	−	0.323796i	$-0.104959\pi$
$251$	18.0416	+	10.4163i	1.13878	+	0.657472i	0.192648	+	0.981268i	$0.438292\pi$
$252$	−2.74876	+	13.4089i	−0.173155	+	0.844683i
$253$	−0.670726	+	1.16173i	−0.0421682	+	0.0730374i
$254$	−9.96732	−	7.18665i	−0.625405	−	0.450931i
$255$			1.23573i			0.0773847i
$256$	−15.5474	+	3.77875i	−0.971711	+	0.236172i
$257$	−0.0721456	−	0.124960i	−0.00450032	−	0.00779478i	0.863766	−	0.503892i	$-0.168099\pi$
$257$	−0.0721456	−	0.124960i	−0.00450032	−	0.00779478i	−0.868267	+	0.496098i	$0.834766\pi$
$258$	−2.14312	+	0.963498i	−0.133425	+	0.0599848i
$259$		−	36.1391i		−	2.24557i
$260$	5.14126	+	5.05642i	0.318848	+	0.313586i
$261$		−	5.29074i		−	0.327489i
$262$	−10.7351	−	23.8782i	−0.663217	−	1.47520i
$263$	−12.7246	−	22.0397i	−0.784632	−	1.35902i	−0.929218	−	0.369531i	$-0.879518\pi$
$263$	−12.7246	−	22.0397i	−0.784632	−	1.35902i	0.144586	−	0.989492i	$-0.453815\pi$
$264$	−2.91262	+	2.68043i	−0.179260	+	0.164969i
$265$		−	8.10029i		−	0.497597i
$266$	−22.3844	+	31.0454i	−1.37247	+	1.90351i
$267$	−8.55184	+	14.8122i	−0.523364	+	0.906494i
$268$	20.4985	+	4.20208i	1.25215	+	0.256683i
$269$	19.4744	+	11.2436i	1.18738	+	0.685533i	0.957710	−	0.287736i	$-0.0929025\pi$
$269$	19.4744	+	11.2436i	1.18738	+	0.685533i	0.229668	+	0.973269i	$0.426236\pi$
$270$	−3.19451	−	7.10559i	−0.194412	−	0.432433i
$271$	10.8229	−	6.24860i	0.657444	−	0.379575i	−0.133859	−	0.991000i	$-0.542737\pi$
$271$	10.8229	−	6.24860i	0.657444	−	0.379575i	0.791302	+	0.611425i	$0.209403\pi$
$272$	−3.71546	−	1.59012i	−0.225283	−	0.0964151i
$273$	1.02864	−	20.0390i	0.0622559	−	1.21281i
$274$	−2.31045	−	0.234378i	−0.139579	−	0.0141593i
$275$	−0.572114	−	0.990930i	−0.0344998	−	0.0597554i
$276$	−2.72091	+	0.905926i	−0.163779	+	0.0545304i
$277$	12.5777	+	7.26175i	0.755722	+	0.436316i	0.827758	−	0.561086i	$-0.189616\pi$
$277$	12.5777	+	7.26175i	0.755722	+	0.436316i	−0.0720355	+	0.997402i	$0.522949\pi$
$278$	−23.7492	−	2.40918i	−1.42438	−	0.144493i
$279$	1.06045	+	0.612252i	0.0634875	+	0.0366546i
$280$	−9.46991	+	8.71497i	−0.565935	+	0.520819i
$281$		−	9.66247i		−	0.576414i	−0.957568	−	0.288207i	$-0.906941\pi$
$281$		−	9.66247i		−	0.576414i	0.957568	−	0.288207i	$-0.0930592\pi$
$282$	−12.7076	−	9.16246i	−0.756727	−	0.545617i
$283$	12.9189	−	7.45873i	0.767949	−	0.443376i	−0.0641934	−	0.997937i	$-0.520447\pi$
$283$	12.9189	−	7.45873i	0.767949	−	0.443376i	0.832143	+	0.554562i	$0.187114\pi$
$284$	−11.0471	+	3.67812i	−0.655523	+	0.218256i
$285$		−	7.27464i		−	0.430912i
$286$	−3.65040	+	4.55140i	−0.215853	+	0.269130i
$287$	−40.1154			−2.36794
$288$	8.50711	−	0.154126i	0.501286	−	0.00908197i
$289$	7.98959	+	13.8384i	0.469976	+	0.814022i
$290$	2.90936	−	4.03506i	0.170844	−	0.236947i
$291$	6.16521			0.361411
$292$	21.8095	+	19.3530i	1.27630	+	1.13255i
$293$	0.439423	−	0.761103i	0.0256714	−	0.0444641i	−0.852904	−	0.522067i	$-0.825161\pi$
$293$	0.439423	−	0.761103i	0.0256714	−	0.0444641i	0.878576	+	0.477603i	$0.158494\pi$
$294$	23.5820	+	2.39222i	1.37533	+	0.139517i
$295$	−3.14969	+	5.45542i	−0.183382	+	0.317627i
$296$	−21.9216	+	4.90920i	−1.27417	+	0.285341i
$297$	5.45886	−	3.15168i	0.316755	−	0.182879i
$298$	−2.11106	+	20.8104i	−0.122291	+	1.20552i
$299$	−3.76424	+	1.92307i	−0.217692	+	0.111214i
$300$	0.491229	−	2.39630i	0.0283611	−	0.138351i
$301$	−3.09065	−	5.35316i	−0.178142	−	0.308551i
$302$	4.20203	+	9.34663i	0.241800	+	0.537838i
$303$	4.91069	−	8.50556i	0.282112	−	0.488632i
$304$	21.8725	+	9.36086i	1.25447	+	0.536882i
$305$	−10.5468	−	6.08920i	−0.603909	−	0.348667i
$306$	1.74327	+	1.25693i	0.0996560	+	0.0718541i
$307$	−18.9672			−1.08251			−0.541257	−	0.840857i	$-0.682052\pi$
$307$	−18.9672			−1.08251			−0.541257	+	0.840857i	$0.682052\pi$
$308$	−7.78849	−	6.91126i	−0.443790	−	0.393805i
$309$	6.45857	−	3.72886i	0.367415	−	0.212127i
$310$	0.472093	+	1.05008i	0.0268131	+	0.0596406i
$311$	7.42874			0.421245			0.210623	−	0.977567i	$-0.432451\pi$
$311$	7.42874			0.421245			0.210623	+	0.977567i	$0.432451\pi$
$312$	−12.2952	+	2.09817i	−0.696076	+	0.118785i
$313$	18.3767			1.03871			0.519356	−	0.854558i	$-0.326172\pi$
$313$	18.3767			1.03871			0.519356	+	0.854558i	$0.326172\pi$
$314$	4.64229	+	10.3259i	0.261980	+	0.582725i
$315$	5.92698	−	3.42194i	0.333947	−	0.192805i
$316$	−7.43608	+	8.37993i	−0.418312	+	0.471408i
$317$	−9.12947			−0.512762			−0.256381	−	0.966576i	$-0.582530\pi$
$317$	−9.12947			−0.512762			−0.256381	+	0.966576i	$0.582530\pi$
$318$	11.3648	+	8.19428i	0.637307	+	0.459512i
$319$	3.48563	+	2.01243i	0.195158	+	0.112674i
$320$	6.57282	+	4.56049i	0.367432	+	0.254939i
$321$	−6.13681	+	10.6293i	−0.342523	+	0.593268i
$322$	−3.09337	−	6.88062i	−0.172387	−	0.383442i
$323$	3.00473	+	5.20434i	0.167188	+	0.289577i
$324$	4.36004	+	0.893784i	0.242224	+	0.0496547i
$325$	0.184836	−	3.60081i	0.0102529	−	0.199737i
$326$	−0.449172	+	4.42785i	−0.0248773	+	0.245236i
$327$	8.77409	−	5.06573i	0.485208	−	0.280135i
$328$	5.44935	+	24.3336i	0.300890	+	1.34360i
$329$	20.6061	−	35.6909i	1.13605	−	1.96770i
$330$	1.96904	+	0.199745i	0.108392	+	0.0109956i
$331$	0.660141	−	1.14340i	0.0362846	−	0.0628468i	−0.847313	−	0.531094i	$-0.821781\pi$
$331$	0.660141	−	1.14340i	0.0362846	−	0.0628468i	0.883597	+	0.468247i	$0.155114\pi$
$332$	3.07506	−	3.46538i	0.168766	−	0.190187i
$333$	11.9462			0.654649
$334$	9.38088	−	13.0105i	0.513299	−	0.711905i
$335$	−5.23119	−	9.06069i	−0.285811	−	0.495038i
$336$	−2.64744	−	22.1025i	−0.144430	−	1.20579i
$337$	−8.88371			−0.483926			−0.241963	−	0.970285i	$-0.577791\pi$
$337$	−8.88371			−0.483926			−0.241963	+	0.970285i	$0.577791\pi$
$338$	−17.4519	+	5.78199i	−0.949258	+	0.314499i
$339$		−	13.3541i		−	0.725294i
$340$	0.638344	+	1.91724i	0.0346190	+	0.103977i
$341$	−0.806724	+	0.465762i	−0.0436866	+	0.0252224i
$342$	−10.2624	−	7.39944i	−0.554929	−	0.400116i
$343$			30.5029i			1.64700i
$344$	−2.82733	+	2.60194i	−0.152439	+	0.140287i
$345$	1.24178	+	0.716940i	0.0668550	+	0.0385988i
$346$	27.6757	+	2.80749i	1.48785	+	0.150932i
$347$	−11.9243	−	6.88451i	−0.640131	−	0.369580i	0.144534	−	0.989500i	$-0.453832\pi$
$347$	−11.9243	−	6.88451i	−0.640131	−	0.369580i	−0.784665	+	0.619920i	$0.787165\pi$
$348$	2.71812	+	8.16375i	0.145707	+	0.437623i
$349$	3.90021	+	6.75535i	0.208773	+	0.361606i	0.951328	−	0.308179i	$-0.0997196\pi$
$349$	3.90021	+	6.75535i	0.208773	+	0.361606i	−0.742555	+	0.669785i	$0.766386\pi$
$350$	6.40201	+	0.649436i	0.342202	+	0.0347138i
$351$	19.8362	+	1.01823i	1.05878	+	0.0543491i
$352$	−3.13429	+	5.66325i	−0.167058	+	0.301852i
$353$	11.9984	−	6.92729i	0.638611	−	0.368702i	−0.145468	−	0.989363i	$-0.546469\pi$
$353$	11.9984	−	6.92729i	0.638611	−	0.368702i	0.784079	+	0.620660i	$0.213135\pi$
$354$	−4.46780	−	9.93778i	−0.237461	−	0.528187i
$355$	5.04169	+	2.91082i	0.267585	+	0.154490i
$356$	−5.61659	+	27.3987i	−0.297679	+	1.45213i
$357$	2.81138	−	4.86945i	0.148794	−	0.257719i
$358$	2.57723	−	3.57441i	0.136211	−	0.188914i
$359$		−	8.80624i		−	0.464775i	−0.972623	−	0.232388i	$-0.925346\pi$
$359$		−	8.80624i		−	0.464775i	0.972623	−	0.232388i	$-0.0746538\pi$
$360$	−2.88084	−	3.13040i	−0.151834	−	0.164986i
$361$	−8.18852	−	14.1829i	−0.430975	−	0.746470i
$362$	−14.3464	−	31.9110i	−0.754032	−	1.67720i
$363$		−	11.8524i		−	0.622092i
$364$	−8.75561	−	31.6217i	−0.458919	−	1.65743i
$365$		−	14.5790i		−	0.763101i
$366$	19.2124	−	8.63746i	1.00425	−	0.451487i
$367$	10.6973	+	18.5283i	0.558397	+	0.967172i	0.997631	+	0.0687988i	$0.0219166\pi$
$367$	10.6973	+	18.5283i	0.558397	+	0.967172i	−0.439234	+	0.898373i	$0.644750\pi$
$368$	−3.75350	+	2.81108i	−0.195665	+	0.146538i
$369$		−	13.2607i		−	0.690322i
$370$	9.11096	+	6.56920i	0.473656	+	0.341516i
$371$	−18.4287	+	31.9195i	−0.956771	+	1.65718i
$372$	−1.95085	−	0.399914i	−0.101147	−	0.0207346i
$373$	−24.6923	−	14.2561i	−1.27852	−	0.738154i	−0.301945	−	0.953325i	$-0.597636\pi$
$373$	−24.6923	−	14.2561i	−1.27852	−	0.738154i	−0.976576	+	0.215171i	$0.930969\pi$
$374$	−1.49117	+	0.670397i	−0.0771068	+	0.0346654i
$375$	−1.05921	+	0.611534i	−0.0546973	+	0.0315795i
$376$	−24.4489	−	7.65115i	−1.26085	−	0.394578i
$377$	5.76992	+	11.2941i	0.297166	+	0.581678i
$378$	−3.57763	+	35.2675i	−0.184013	+	1.81397i
$379$	−1.37039	−	2.37358i	−0.0703921	−	0.121923i	0.828681	−	0.559721i	$-0.189092\pi$
$379$	−1.37039	−	2.37358i	−0.0703921	−	0.121923i	−0.899073	+	0.437798i	$0.855758\pi$
$380$	−3.75786	−	11.2866i	−0.192774	−	0.578989i
$381$	−9.20339	−	5.31358i	−0.471504	−	0.272223i
$382$	0.388886	−	3.83356i	0.0198972	−	0.196142i
$383$	26.2337	+	15.1460i	1.34048	+	0.773926i	0.986878	−	0.161470i	$-0.0516236\pi$
$383$	26.2337	+	15.1460i	1.34048	+	0.773926i	0.353601	+	0.935396i	$0.384957\pi$
$384$	−13.0475	+	4.60835i	−0.665828	+	0.235169i
$385$			5.20639i			0.265342i
$386$	3.71079	−	5.14658i	0.188874	−	0.261954i
$387$	1.76955	−	1.02165i	0.0899515	−	0.0519335i
$388$	9.56529	−	3.18476i	0.485604	−	0.161682i
$389$			2.87672i			0.145856i	0.997337	+	0.0729278i	$0.0232343\pi$
$389$			2.87672i			0.145856i	−0.997337	+	0.0729278i	$0.976766\pi$
$390$	4.86501	+	3.90192i	0.246349	+	0.197581i
$391$	−1.18450			−0.0599030
$392$	37.8232	−	8.47026i	1.91036	−	0.427813i
$393$	−11.3209	−	19.6084i	−0.571065	−	0.989113i
$394$	−25.5569	−	18.4271i	−1.28754	−	0.928342i
$395$	5.60175			0.281855
$396$	2.28460	−	2.57458i	0.114806	−	0.129378i
$397$	−1.96447	+	3.40257i	−0.0985941	+	0.170770i	−0.911103	−	0.412179i	$-0.864768\pi$
$397$	−1.96447	+	3.40257i	−0.0985941	+	0.170770i	0.812509	+	0.582949i	$0.198101\pi$
$398$	3.34409	−	32.9654i	0.167624	−	1.65241i
$399$	−16.5503	+	28.6659i	−0.828551	+	1.43509i
$400$	−0.475720	−	3.97161i	−0.0237860	−	0.198581i
$401$	12.3010	−	7.10197i	0.614281	−	0.354655i	−0.160358	−	0.987059i	$-0.551265\pi$
$401$	12.3010	−	7.10197i	0.614281	−	0.354655i	0.774639	+	0.632404i	$0.217932\pi$
$402$	18.0042	+	1.82639i	0.897966	+	0.0910920i
$403$	−2.93145	−	0.150477i	−0.146026	−	0.00749577i
$404$	3.22519	−	15.7331i	0.160459	−	0.782749i
$405$	−1.11268	−	1.92721i	−0.0552893	−	0.0957639i
$406$	−20.6445	+	9.28128i	−1.02457	+	0.460622i
$407$	−4.54397	+	7.87038i	−0.225236	+	0.390120i
$408$	−3.33566	−	1.04388i	−0.165140	−	0.0516796i
$409$	1.48633	+	0.858133i	0.0734943	+	0.0424319i	0.536297	−	0.844029i	$-0.319823\pi$
$409$	1.48633	+	0.858133i	0.0734943	+	0.0424319i	−0.462803	+	0.886461i	$0.653156\pi$
$410$	7.29200	−	10.1134i	0.360126	−	0.499466i
$411$	−2.00842			−0.0990683
$412$	8.09423	−	9.12161i	0.398774	−	0.449390i
$413$	24.8229	−	14.3315i	1.22146	−	0.705208i
$414$	2.27448	−	1.02255i	0.111784	−	0.0502557i
$415$	−2.31651			−0.113713
$416$	−17.9920	+	9.60661i	−0.882132	+	0.471003i
$417$	−20.6447			−1.01098
$418$	8.77838	−	3.94656i	0.429365	−	0.193032i
$419$	7.27337	−	4.19928i	0.355327	−	0.205148i	−0.311702	−	0.950180i	$-0.600899\pi$
$419$	7.27337	−	4.19928i	0.355327	−	0.205148i	0.667029	+	0.745032i	$0.267566\pi$
$420$	−7.38746	+	8.32514i	−0.360471	+	0.406225i
$421$	7.41738			0.361501			0.180750	−	0.983529i	$-0.442147\pi$
$421$	7.41738			0.361501			0.180750	+	0.983529i	$0.442147\pi$
$422$	10.2419	−	14.2048i	0.498569	−	0.691476i
$423$	11.7981	+	6.81162i	0.573641	+	0.331192i
$424$	21.8654	+	6.84266i	1.06188	+	0.332309i
$425$	0.505178	−	0.874994i	0.0245047	−	0.0424434i
$426$	−9.18412	+	4.12897i	−0.444972	+	0.200049i
$427$	27.7067	+	47.9894i	1.34082	+	2.32237i
$428$	−4.03047	+	19.6614i	−0.194820	+	0.950368i
$429$	−2.74363	+	4.23476i	−0.132464	+	0.204456i
$430$	1.91138	+	0.193895i	0.0921749	+	0.00935045i
$431$	−26.0610	+	15.0463i	−1.25531	+	0.724755i	−0.972160	−	0.234320i	$-0.924714\pi$
$431$	−26.0610	+	15.0463i	−1.25531	+	0.724755i	−0.283153	+	0.959075i	$0.591380\pi$
$432$	21.8789	−	2.62066i	1.05265	−	0.126086i
$433$	−20.6058	+	35.6904i	−0.990254	+	1.71517i	−0.374510	+	0.927223i	$0.622189\pi$
$433$	−20.6058	+	35.6904i	−0.990254	+	1.71517i	−0.615744	+	0.787947i	$0.711144\pi$
$434$	0.528711	−	5.21192i	0.0253789	−	0.250180i
$435$	2.15109	−	3.72580i	0.103137	−	0.178638i
$436$	10.9962	−	12.3919i	0.526621	−	0.593464i
$437$	6.97305			0.333566
$438$	20.4546	+	14.7482i	0.977358	+	0.704696i
$439$	16.9420	+	29.3445i	0.808599	+	1.40053i	0.913834	+	0.406088i	$0.133107\pi$
$439$	16.9420	+	29.3445i	0.808599	+	1.40053i	−0.105235	+	0.994447i	$0.533559\pi$
$440$	3.15814	−	0.707246i	0.150559	−	0.0337166i
$441$	−20.6119			−0.981517
$442$	−5.09213	−	0.782018i	−0.242208	−	0.0371968i
$443$		−	36.2565i		−	1.72260i	−0.508098	−	0.861299i	$-0.669651\pi$
$443$		−	36.2565i		−	1.72260i	0.508098	−	0.861299i	$-0.330349\pi$
$444$	−18.4334	+	6.13739i	−0.874809	+	0.291267i
$445$	12.1107	−	6.99213i	0.574103	−	0.331459i
$446$	−18.6297	+	25.8379i	−0.882140	+	1.22346i
$447$			18.0901i			0.855630i
$448$	−15.5250	−	32.9244i	−0.733487	−	1.55553i
$449$	1.59884	+	0.923091i	0.0754539	+	0.0435633i	0.537252	−	0.843422i	$-0.319462\pi$
$449$	1.59884	+	0.923091i	0.0754539	+	0.0435633i	−0.461798	+	0.886985i	$0.652796\pi$
$450$	−0.214679	+	2.11626i	−0.0101201	+	0.0997617i
$451$	8.73635	+	5.04393i	0.411379	+	0.237510i
$452$	−6.89833	−	20.7188i	−0.324470	−	0.974531i
$453$	4.43133	+	7.67529i	0.208202	+	0.360617i
$454$	−2.32223	+	22.8921i	−0.108988	+	1.07438i
$455$	−8.92044	+	13.7686i	−0.418197	+	0.645482i
$456$	19.6367	+	6.14520i	0.919572	+	0.287775i
$457$	−3.05167	+	1.76189i	−0.142751	+	0.0824175i	−0.569675	−	0.821870i	$-0.692931\pi$
$457$	−3.05167	+	1.76189i	−0.142751	+	0.0824175i	0.426923	+	0.904288i	$0.359597\pi$
$458$	7.61444	−	3.42328i	0.355799	−	0.159959i
$459$	4.82019	+	2.78294i	0.224987	+	0.129896i
$460$	2.29696	+	0.470865i	0.107096	+	0.0219542i
$461$	−18.8888	+	32.7164i	−0.879740	+	1.52375i	−0.0281134	+	0.999605i	$0.508950\pi$
$461$	−18.8888	+	32.7164i	−0.879740	+	1.52375i	−0.851626	+	0.524149i	$0.824383\pi$
$462$	−7.30464	−	5.26680i	−0.339843	−	0.245034i
$463$		−	0.0534854i		−	0.00248568i	−0.999999	−	0.00124284i	$-0.999604\pi$
$463$		−	0.0534854i		−	0.00248568i	0.999999	−	0.00124284i	$-0.000395608\pi$
$464$	8.43431	+	11.2619i	0.391553	+	0.522822i
$465$	0.497854	+	0.862309i	0.0230874	+	0.0399886i
$466$	−0.265448	+	0.119339i	−0.0122967	+	0.00552829i
$467$		−	1.74333i		−	0.0806719i	−0.999186	−	0.0403360i	$-0.987157\pi$
$467$		−	1.74333i		−	0.0806719i	0.999186	−	0.0403360i	$-0.0128428\pi$
$468$	10.4530	−	2.89428i	0.483188	−	0.133788i
$469$			47.6053i			2.19821i
$470$	5.25227	+	11.6827i	0.242269	+	0.538883i
$471$	4.89562	+	8.47947i	0.225578	+	0.390713i
$472$	−12.0653	−	13.1105i	−0.555352	−	0.603459i
$473$			1.55442i			0.0714722i
$474$	−5.66675	+	7.85934i	−0.260283	+	0.360991i
$475$	−2.97393	+	5.15100i	−0.136453	+	0.236344i
$476$	1.84643	−	9.00721i	0.0846309	−	0.412845i
$477$	−10.5514	−	6.09184i	−0.483115	−	0.278926i
$478$	−12.9580	−	28.8227i	−0.592687	−	1.31832i
$479$	−35.5001	+	20.4960i	−1.62204	+	0.936485i	−0.635666	+	0.771964i	$0.719274\pi$
$479$	−35.5001	+	20.4960i	−1.62204	+	0.936485i	−0.986374	+	0.164521i	$0.947392\pi$
$480$	6.05347	+	3.35025i	0.276302	+	0.152917i
$481$	−25.5016	+	13.0282i	−1.16277	+	0.594035i
$482$	−8.47624	−	0.859851i	−0.386082	−	0.0391652i
$483$	−3.26217	−	5.65025i	−0.148434	−	0.257095i
$484$	−6.12262	−	18.3890i	−0.278301	−	0.835864i
$485$	−4.36544	−	2.52039i	−0.198224	−	0.114445i
$486$	−19.4231	−	1.97033i	−0.881052	−	0.0893761i
$487$	9.82918	+	5.67488i	0.445402	+	0.257153i	0.705887	−	0.708325i	$-0.250549\pi$
$487$	9.82918	+	5.67488i	0.445402	+	0.257153i	−0.260484	+	0.965478i	$0.583882\pi$
$488$	25.3461	−	23.3256i	1.14737	−	1.05590i
$489$			3.84903i			0.174059i
$490$	−15.7199	−	11.3344i	−0.710154	−	0.512036i
$491$	−3.97077	+	2.29253i	−0.179198	+	0.103460i	−0.586916	−	0.809648i	$-0.699658\pi$
$491$	−3.97077	+	2.29253i	−0.179198	+	0.103460i	0.407718	+	0.913108i	$0.366325\pi$
$492$	6.81267	+	20.4615i	0.307139	+	0.922478i
$493$			3.55396i			0.160062i
$494$	29.9768	+	4.60366i	1.34872	+	0.207128i
$495$	−1.72104			−0.0773550
$496$	−3.23332	+	0.387287i	−0.145180	+	0.0173897i
$497$	−13.2446	−	22.9404i	−0.594103	−	1.02902i
$498$	2.34339	−	3.25009i	0.105010	−	0.145640i
$499$	−26.8211			−1.20068			−0.600338	−	0.799746i	$-0.704967\pi$
$499$	−26.8211			−1.20068			−0.600338	+	0.799746i	$0.704967\pi$
$500$	−1.32746	+	1.49595i	−0.0593657	+	0.0669008i
$501$	6.93593	−	12.0134i	0.309874	−	0.536718i
$502$	29.3114	+	2.97342i	1.30823	+	0.132710i
$503$	1.88459	−	3.26420i	0.0840296	−	0.145543i	−0.820948	−	0.571003i	$-0.806554\pi$
$503$	1.88459	−	3.26420i	0.0840296	−	0.145543i	0.904977	+	0.425460i	$0.139888\pi$
$504$	4.23019	+	18.8896i	0.188428	+	0.841408i
$505$	−6.95428	+	4.01506i	−0.309462	+	0.178668i
$506$	−0.191464	+	1.88741i	−0.00851161	+	0.0839057i
$507$	−14.5114	+	6.49822i	−0.644472	+	0.288596i
$508$	−17.0239	−	3.48980i	−0.755312	−	0.154835i
$509$	−8.23498	−	14.2634i	−0.365009	−	0.632214i	0.623769	−	0.781609i	$-0.285601\pi$
$509$	−8.23498	−	14.2634i	−0.365009	−	0.632214i	−0.988778	+	0.149395i	$0.952267\pi$
$510$	0.716589	+	1.59392i	0.0317311	+	0.0705799i
$511$	−33.1683	+	57.4491i	−1.46728	+	2.54140i
$512$	−17.8626	+	13.8898i	−0.789424	+	0.613848i
$513$	−28.3760	−	16.3829i	−1.25283	−	0.723321i
$514$	−0.165520	−	0.119344i	−0.00730079	−	0.00526403i
$515$	−6.09755			−0.268690
$516$	−2.20560	+	2.48555i	−0.0970959	+	0.109420i
$517$	−8.97522	+	5.18185i	−0.394730	+	0.227897i
$518$	−20.9567	−	46.6142i	−0.920783	−	2.04811i
$519$	24.0579			1.05602
$520$	9.56365	+	3.54069i	0.419394	+	0.155270i
$521$	31.9015			1.39763			0.698815	−	0.715302i	$-0.253711\pi$
$521$	31.9015			1.39763			0.698815	+	0.715302i	$0.253711\pi$
$522$	−3.06804	−	6.82429i	−0.134285	−	0.298691i
$523$	30.2068	−	17.4399i	1.32085	−	0.762594i	0.336988	−	0.941509i	$-0.390592\pi$
$523$	30.2068	−	17.4399i	1.32085	−	0.762594i	0.983865	+	0.178915i	$0.0572586\pi$
$524$	−27.6935	−	24.5743i	−1.20979	−	1.07353i
$525$	5.56512			0.242882
$526$	−29.1935	−	21.0491i	−1.27290	−	0.917785i
$527$	−0.712339	−	0.411269i	−0.0310300	−	0.0179152i
$528$	−2.20251	+	5.14637i	−0.0958520	+	0.223967i
$529$	10.8128	−	18.7283i	0.470121	−	0.814273i
$530$	−4.69727	−	10.4482i	−0.204036	−	0.453841i
$531$	4.73746	+	8.20553i	0.205588	+	0.356090i
$532$	−10.8697	+	53.0245i	−0.471263	+	2.29890i
$533$	14.4617	+	28.3075i	0.626405	+	1.22613i
$534$	−2.44119	+	24.0648i	−0.105641	+	1.04138i
$535$	8.69066	−	5.01756i	0.375730	−	0.216928i
$536$	28.8769	−	6.46679i	1.24729	−	0.279323i
$537$	1.90552	−	3.30046i	0.0822293	−	0.142425i
$538$	31.6393	+	3.20957i	1.36407	+	0.138374i
$539$	7.84010	−	13.5794i	0.337697	−	0.584908i
$540$	−8.24092	−	7.31273i	−0.354633	−	0.314690i
$541$	−17.8535			−0.767582			−0.383791	−	0.923420i	$-0.625382\pi$
$541$	−17.8535			−0.767582			−0.383791	+	0.923420i	$0.625382\pi$
$542$	10.3365	−	14.3359i	0.443989	−	0.615778i
$543$	−15.1293	−	26.2047i	−0.649261	−	1.12455i
$544$	−5.71450	+	0.103532i	−0.245007	+	0.00443888i
$545$	−8.28364			−0.354832
$546$	−10.2936	−	26.4439i	−0.440525	−	1.13169i
$547$			45.5394i			1.94712i	0.228424	+	0.973562i	$0.426643\pi$
$547$			45.5394i			1.94712i	−0.228424	+	0.973562i	$0.573357\pi$
$548$	−3.11606	+	1.03749i	−0.133112	+	0.0443195i
$549$	−15.8635	+	9.15880i	−0.677038	+	0.390888i
$550$	−1.31257	−	0.946395i	−0.0559684	−	0.0403544i
$551$		−	20.9218i		−	0.891298i
$552$	−2.98424	+	2.74634i	−0.127018	+	0.116892i
$553$	−22.0739	−	12.7444i	−0.938677	−	0.541946i
$554$	20.4345	+	2.07292i	0.868177	+	0.0880701i
$555$	8.41267	+	4.85706i	0.357098	+	0.206171i
$556$	−32.0302	+	10.6644i	−1.35838	+	0.452273i
$557$	−6.58799	−	11.4107i	−0.279142	−	0.483488i	0.692030	−	0.721869i	$-0.256717\pi$
$557$	−6.58799	−	11.4107i	−0.279142	−	0.483488i	−0.971172	+	0.238381i	$0.923383\pi$
$558$	1.72287	+	0.174772i	0.0729348	+	0.00739869i
$559$	−2.66328	+	4.11074i	−0.112645	+	0.173866i
$560$	−7.16109	+	16.7326i	−0.302611	+	0.707080i
$561$	−1.22453	+	0.706981i	−0.0516996	+	0.0298488i
$562$	−5.60316	−	12.4632i	−0.236355	−	0.525728i
$563$	36.2657	+	20.9380i	1.52842	+	0.882431i	0.999429	+	0.0338006i	$0.0107611\pi$
$563$	36.2657	+	20.9380i	1.52842	+	0.882431i	0.528986	+	0.848630i	$0.322572\pi$
$564$	−21.7042	−	4.44924i	−0.913912	−	0.187347i
$565$	−5.45926	+	9.45571i	−0.229673	+	0.397805i
$566$	12.3383	−	17.1122i	0.518617	−	0.719281i
$567$			10.1257i			0.425238i
$568$	−12.1162	+	11.1503i	−0.508385	+	0.467857i
$569$	2.92320	+	5.06313i	0.122547	+	0.212257i	0.920771	−	0.390103i	$-0.127560\pi$
$569$	2.92320	+	5.06313i	0.122547	+	0.212257i	−0.798225	+	0.602360i	$0.794227\pi$
$570$	−4.21849	−	9.38323i	−0.176693	−	0.393020i
$571$		−	27.1617i		−	1.13668i	−0.822794	−	0.568340i	$-0.807586\pi$
$571$		−	27.1617i		−	1.13668i	0.822794	−	0.568340i	$-0.192414\pi$
$572$	−2.06918	+	7.98748i	−0.0865166	+	0.333973i
$573$		−	3.33243i		−	0.139214i
$574$	−51.7431	+	23.2625i	−2.15971	+	0.970958i
$575$	−0.586182	−	1.01530i	−0.0244455	−	0.0423408i
$576$	10.8836	−	5.13198i	0.453482	−	0.213833i
$577$			18.6263i			0.775423i	0.921781	+	0.387711i	$0.126734\pi$
$577$			18.6263i			0.775423i	−0.921781	+	0.387711i	$0.873266\pi$
$578$	18.3301	+	13.2164i	0.762434	+	0.549731i
$579$	2.74364	−	4.75213i	0.114022	−	0.197492i
$580$	1.41277	−	6.89175i	0.0586621	−	0.286164i
$581$	9.12828	+	5.27021i	0.378705	+	0.218645i
$582$	7.95223	−	3.57514i	0.329631	−	0.148194i
$583$	8.02682	−	4.63429i	0.332437	−	0.191933i
$584$	39.3537	+	12.3155i	1.62847	+	0.509620i
$585$	−4.55138	−	2.94876i	−0.188177	−	0.121916i
$586$	0.125437	−	1.23653i	0.00518174	−	0.0510806i
$587$	−5.08980	−	8.81578i	−0.210078	−	0.363866i	0.741660	−	0.670775i	$-0.234039\pi$
$587$	−5.08980	−	8.81578i	−0.210078	−	0.363866i	−0.951739	+	0.306909i	$0.900705\pi$
$588$	31.8047	−	10.5894i	1.31160	−	0.436698i
$589$	4.19347	+	2.42110i	0.172789	+	0.0997597i
$590$	−0.899103	+	8.86318i	−0.0370155	+	0.364891i
$591$	−23.5981	−	13.6244i	−0.970698	−	0.560433i
$592$	−25.4289	+	19.0443i	−1.04512	+	0.782714i
$593$			36.1001i			1.48246i	0.671254	+	0.741228i	$0.265756\pi$
$593$			36.1001i			1.48246i	−0.671254	+	0.741228i	$0.734244\pi$
$594$	5.21352	−	7.23075i	0.213913	−	0.296681i
$595$	−3.98134	+	2.29863i	−0.163219	+	0.0942346i
$596$	9.34479	+	28.0667i	0.382777	+	1.14965i
$597$		−	28.6561i		−	1.17282i
$598$	−3.74016	+	4.66332i	−0.152946	+	0.190697i
$599$	−36.0020			−1.47100			−0.735500	−	0.677524i	$-0.763053\pi$
$599$	−36.0020			−1.47100			−0.735500	+	0.677524i	$0.763053\pi$
$600$	−0.755977	−	3.37575i	−0.0308626	−	0.137814i
$601$	−7.83301	−	13.5672i	−0.319515	−	0.553416i	0.660872	−	0.750499i	$-0.270187\pi$
$601$	−7.83301	−	13.5672i	−0.319515	−	0.553416i	−0.980387	+	0.197082i	$0.936853\pi$
$602$	−7.09073	−	5.11257i	−0.288997	−	0.208373i
$603$	−15.7365			−0.640841
$604$	10.8400	+	9.61909i	0.441074	+	0.391395i
$605$	−4.84537	+	8.39243i	−0.196992	+	0.341201i
$606$	1.40179	−	13.8186i	0.0569440	−	0.561342i
$607$	7.69440	−	13.3271i	0.312306	−	0.540930i	−0.666555	−	0.745456i	$-0.732232\pi$
$607$	7.69440	−	13.3271i	0.312306	−	0.540930i	0.978861	+	0.204526i	$0.0655652\pi$
$608$	33.6407	−	0.609479i	1.36431	−	0.0247176i
$609$	−16.9529	+	9.78775i	−0.686966	+	0.396620i
$610$	−17.1349	−	1.73821i	−0.693773	−	0.0703781i
$611$	−32.6139	−	1.67413i	−1.31942	−	0.0677280i
$612$	2.97745	+	0.610360i	0.120356	+	0.0246724i
$613$	−2.05756	−	3.56380i	−0.0831040	−	0.143940i	0.821478	−	0.570241i	$-0.193150\pi$
$613$	−2.05756	−	3.56380i	−0.0831040	−	0.143940i	−0.904582	+	0.426300i	$0.859817\pi$
$614$	−24.4649	+	10.9989i	−0.987325	+	0.443878i
$615$	5.39147	−	9.33830i	0.217405	−	0.376557i
$616$	−14.0538	−	4.39806i	−0.566244	−	0.177203i
$617$	41.2096	+	23.7924i	1.65904	+	0.957845i	0.973160	+	0.230128i	$0.0739143\pi$
$617$	41.2096	+	23.7924i	1.65904	+	0.957845i	0.685877	+	0.727718i	$0.259419\pi$
$618$	6.16830	−	8.55495i	0.248125	−	0.344130i
$619$	−19.3757			−0.778775			−0.389387	−	0.921074i	$-0.627313\pi$
$619$	−19.3757			−0.778775			−0.389387	+	0.921074i	$0.627313\pi$
$620$	1.21786	+	1.08069i	0.0489105	+	0.0434017i
$621$	5.59309	−	3.22917i	0.224443	−	0.129582i
$622$	9.58201	−	4.30785i	0.384204	−	0.172729i
$623$	−63.6302			−2.54929
$624$	−14.6423	+	9.83617i	−0.586160	+	0.393762i
$625$	1.00000			0.0400000
$626$	23.7033	−	10.6565i	0.947374	−	0.425918i
$627$	7.20866	−	4.16192i	0.287886	−	0.166211i
$628$	11.9758	+	10.6269i	0.477886	+	0.424060i
$629$	−8.02467			−0.319965
$630$	5.66060	−	7.85080i	0.225524	−	0.312783i
$631$	37.4272	+	21.6086i	1.48996	+	0.860226i	0.999934	−	0.0114845i	$-0.00365572\pi$
$631$	37.4272	+	21.6086i	1.48996	+	0.860226i	0.490021	+	0.871711i	$0.336989\pi$
$632$	−4.73204	+	15.1210i	−0.188230	+	0.601481i
$633$	7.57256	−	13.1161i	0.300982	−	0.521316i
$634$	−11.7757	+	5.29409i	−0.467673	+	0.210255i
$635$	4.34447	+	7.52484i	0.172405	+	0.298614i
$636$	19.4108	+	3.97910i	0.769687	+	0.157782i
$637$	44.0001	−	22.4787i	1.74335	−	0.890638i
$638$	5.66295	+	0.574464i	0.224198	+	0.0227432i
$639$	7.58324	−	4.37818i	0.299988	−	0.173198i
$640$	11.1226	+	2.07086i	0.439658	+	0.0818581i
$641$	−0.375135	+	0.649753i	−0.0148169	+	0.0256637i	−0.873339	−	0.487113i	$-0.838050\pi$
$641$	−0.375135	+	0.649753i	−0.0148169	+	0.0256637i	0.858522	+	0.512777i	$0.171383\pi$
$642$	−1.75180	+	17.2689i	−0.0691380	+	0.681549i
$643$	17.4326	−	30.1942i	0.687475	−	1.19074i	−0.285177	−	0.958475i	$-0.592052\pi$
$643$	17.4326	−	30.1942i	0.687475	−	1.19074i	0.972652	−	0.232267i	$-0.0746144\pi$
$644$	−7.98000	−	7.08120i	−0.314456	−	0.279038i
$645$	1.66152			0.0654223
$646$	6.89361	+	4.97044i	0.271225	+	0.195559i
$647$	1.16225	+	2.01308i	0.0456928	+	0.0791422i	0.887967	−	0.459907i	$-0.152117\pi$
$647$	1.16225	+	2.01308i	0.0456928	+	0.0791422i	−0.842274	+	0.539049i	$0.818784\pi$
$648$	6.14212	−	1.37549i	0.241285	−	0.0540343i
$649$	−7.20792			−0.282936
$650$	−1.84966	−	4.75171i	−0.0725496	−	0.186377i
$651$		−	4.53061i		−	0.177569i
$652$	1.98829	+	5.97175i	0.0778676	+	0.233872i
$653$	4.47325	−	2.58263i	0.175052	−	0.101066i	−0.409914	−	0.912124i	$-0.634441\pi$
$653$	4.47325	−	2.58263i	0.175052	−	0.101066i	0.584966	+	0.811058i	$0.301108\pi$
$654$	8.37976	−	11.6221i	0.327674	−	0.454459i
$655$			18.5123i			0.723336i
$656$	21.1397	+	28.2268i	0.825365	+	1.10207i
$657$	−18.9905	−	10.9642i	−0.740892	−	0.427754i
$658$	5.88218	−	57.9853i	0.229311	−	2.26050i
$659$	7.64399	+	4.41326i	0.297767	+	0.171916i	0.641440	−	0.767174i	$-0.278338\pi$
$659$	7.64399	+	4.41326i	0.297767	+	0.171916i	−0.343672	+	0.939090i	$0.611671\pi$
$660$	2.65561	−	0.884185i	0.103369	−	0.0344169i
$661$	7.48609	+	12.9663i	0.291175	+	0.504330i	0.974088	−	0.226170i	$-0.0726205\pi$
$661$	7.48609	+	12.9663i	0.291175	+	0.504330i	−0.682913	+	0.730500i	$0.739287\pi$
$662$	0.188442	−	1.85763i	0.00732402	−	0.0721988i
$663$	−4.44964	−	0.228408i	−0.172810	−	0.00887064i
$664$	1.95685	−	6.25303i	0.0759407	−	0.242665i
$665$	23.4377	−	13.5318i	0.908877	−	0.524740i
$666$	15.4089	−	6.92749i	0.597083	−	0.268435i
$667$	3.57134	+	2.06191i	0.138283	+	0.0798376i
$668$	4.55531	−	22.2216i	0.176250	−	0.859780i
$669$	−13.7742	+	23.8576i	−0.532541	+	0.922388i
$670$	−12.0017	−	8.65347i	−0.463666	−	0.334313i
$671$		−	13.9349i		−	0.537950i
$672$	−16.2318	−	26.9738i	−0.626156	−	1.04054i
$673$	13.9440	+	24.1518i	0.537503	+	0.930982i	0.999038	+	0.0438600i	$0.0139656\pi$
$673$	13.9440	+	24.1518i	0.537503	+	0.930982i	−0.461535	+	0.887122i	$0.652701\pi$
$674$	−11.4587	+	5.15157i	−0.441373	+	0.198431i
$675$			5.50883i			0.212035i
$676$	−19.1575	+	17.5781i	−0.736827	+	0.676081i
$677$		−	28.4872i		−	1.09485i	−0.836854	−	0.547426i	$-0.815608\pi$
$677$		−	28.4872i		−	1.09485i	0.836854	−	0.547426i	$-0.184392\pi$
$678$	−7.74389	−	17.2248i	−0.297402	−	0.661516i
$679$	11.4681	+	19.8633i	0.440105	+	0.762285i
$680$	1.93516	+	2.10279i	0.0742099	+	0.0806383i
$681$			19.8996i			0.762553i
$682$	−0.770467	+	1.06858i	−0.0295027	+	0.0409179i
$683$	−17.0661	+	29.5594i	−0.653017	+	1.13106i	0.329370	+	0.944201i	$0.393164\pi$
$683$	−17.0661	+	29.5594i	−0.653017	+	1.13106i	−0.982387	+	0.186858i	$0.940170\pi$
$684$	−17.5279	−	3.59313i	−0.670197	−	0.137387i
$685$	1.42212	+	0.821060i	0.0543363	+	0.0313711i
$686$	17.6883	+	39.3443i	0.675343	+	1.50217i
$687$	6.25285	−	3.61009i	0.238561	−	0.137733i
$688$	−2.13801	+	4.99566i	−0.0815109	+	0.190458i
$689$	29.1676	+	1.49723i	1.11120	+	0.0570398i
$690$	2.01746	+	0.204656i	0.0768033	+	0.00779113i
$691$	−19.2910	−	33.4129i	−0.733863	−	1.27109i	−0.955220	−	0.295895i	$-0.904382\pi$
$691$	−19.2910	−	33.4129i	−0.733863	−	1.27109i	0.221358	−	0.975193i	$-0.428951\pi$
$692$	37.3257	−	12.4276i	1.41891	−	0.472426i
$693$	6.78181	+	3.91548i	0.257620	+	0.148737i
$694$	−19.3729	−	1.96524i	−0.735386	−	0.0745994i
$695$	14.6180	+	8.43972i	0.554493	+	0.320137i
$696$	8.24006	+	8.95386i	0.312339	+	0.339395i
$697$			8.90761i			0.337400i
$698$	8.94806	+	6.45175i	0.338689	+	0.244202i
$699$	−0.217982	+	0.125852i	−0.00824482	+	0.00476015i
$700$	8.63427	−	2.87478i	0.326345	−	0.108656i
$701$			36.6408i			1.38390i	0.721943	+	0.691952i	$0.243249\pi$
$701$			36.6408i			1.38390i	−0.721943	+	0.691952i	$0.756751\pi$
$702$	26.1763	−	10.1895i	0.987963	−	0.384576i
$703$	47.2404			1.78171
$704$	−0.758725	+	9.12233i	−0.0285955	+	0.343811i
$705$	5.53889	+	9.59363i	0.208607	+	0.361317i
$706$	11.4592	−	15.8930i	0.431271	−	0.598140i
$707$	36.5381			1.37416
$708$	−11.5256	−	10.2275i	−0.433160	−	0.384372i
$709$	19.5660	−	33.8893i	0.734816	−	1.27274i	−0.219988	−	0.975503i	$-0.570602\pi$
$709$	19.5660	−	33.8893i	0.734816	−	1.27274i	0.954804	−	0.297236i	$-0.0960648\pi$
$710$	8.19101	+	0.830917i	0.307403	+	0.0311838i
$711$	4.21281	−	7.29680i	0.157993	−	0.273652i
$712$	8.64365	+	38.5974i	0.323934	+	1.44650i
$713$	−0.826561	+	0.477215i	−0.0309549	+	0.0178718i
$714$	0.802530	−	7.91118i	0.0300339	−	0.296068i
$715$	3.67390	−	1.87691i	0.137396	−	0.0701926i
$716$	1.25149	−	6.10498i	0.0467703	−	0.228154i
$717$	−13.6652	−	23.6687i	−0.510334	−	0.883925i
$718$	−5.10664	−	11.3588i	−0.190578	−	0.423906i
$719$	1.76172	−	3.05139i	0.0657011	−	0.113798i	−0.831304	−	0.555818i	$-0.812405\pi$
$719$	1.76172	−	3.05139i	0.0657011	−	0.113798i	0.897005	+	0.442021i	$0.145738\pi$
$720$	−5.53116	−	2.36719i	−0.206134	−	0.0882200i
$721$	24.0276	+	13.8723i	0.894834	+	0.516633i
$722$	−18.7865	−	13.5455i	−0.699163	−	0.504111i
$723$	−7.36821			−0.274027
$724$	−37.0097	−	32.8412i	−1.37545	−	1.22053i
$725$	−3.04627	+	1.75877i	−0.113136	+	0.0653189i
$726$	−6.87310	−	15.2879i	−0.255085	−	0.567388i
$727$	−26.8400			−0.995440			−0.497720	−	0.867338i	$-0.665829\pi$
$727$	−26.8400			−0.995440			−0.497720	+	0.867338i	$0.665829\pi$
$728$	−29.6306	−	35.7102i	−1.09818	−	1.32351i
$729$	−23.5602			−0.872599
$730$	−8.45422	−	18.8048i	−0.312905	−	0.695998i
$731$	−1.18867	+	0.686277i	−0.0439644	+	0.0253829i
$732$	19.7725	−	22.2822i	0.730812	−	0.823573i
$733$	23.3750			0.863375			0.431687	−	0.902023i	$-0.357918\pi$
$733$	23.3750			0.863375			0.431687	+	0.902023i	$0.357918\pi$
$734$	24.5424	+	17.6956i	0.905877	+	0.653157i
$735$	−14.5151	−	8.38030i	−0.535398	−	0.309112i
$736$	−3.21136	+	5.80251i	−0.118372	+	0.213883i
$737$	5.98568	−	10.3675i	0.220485	−	0.381892i
$738$	−7.68971	−	17.1043i	−0.283062	−	0.629619i
$739$	−5.89711	−	10.2141i	−0.216929	−	0.375732i	0.736939	−	0.675960i	$-0.236271\pi$
$739$	−5.89711	−	10.2141i	−0.216929	−	0.375732i	−0.953868	+	0.300228i	$0.902937\pi$
$740$	15.5612	+	3.18997i	0.572043	+	0.117266i
$741$	26.1946	+	1.34462i	0.962282	+	0.0493957i
$742$	−5.26062	+	51.8581i	−0.193123	+	1.90377i
$743$	−1.19902	+	0.692253i	−0.0439877	+	0.0253963i	−0.521833	−	0.853048i	$-0.674751\pi$
$743$	−1.19902	+	0.692253i	−0.0439877	+	0.0253963i	0.477845	+	0.878444i	$0.341418\pi$
$744$	−2.74822	+	0.615446i	−0.100755	+	0.0225634i
$745$	7.39536	−	12.8091i	0.270945	−	0.469291i
$746$	−40.1165	−	4.06952i	−1.46877	−	0.148996i
$747$	−1.74214	+	3.01747i	−0.0637414	+	0.110403i
$748$	−1.53464	+	1.72943i	−0.0561121	+	0.0632343i
$749$	−45.6611			−1.66842
$750$	−1.01160	+	1.40301i	−0.0369385	+	0.0512308i
$751$	−7.32831	−	12.6930i	−0.267414	−	0.463175i	0.700779	−	0.713378i	$-0.252836\pi$
$751$	−7.32831	−	12.6930i	−0.267414	−	0.463175i	−0.968193	+	0.250204i	$0.919502\pi$
$752$	−35.9723	+	4.30877i	−1.31178	+	0.157125i
$753$	25.4797			0.928533
$754$	13.9917	+	11.2219i	0.509548	+	0.408677i
$755$		−	7.24626i		−	0.263718i
$756$	15.8367	+	47.5647i	0.575974	+	1.72991i
$757$	−23.8763	+	13.7850i	−0.867797	+	0.501023i	−0.866616	−	0.498976i	$-0.833709\pi$
$757$	−23.8763	+	13.7850i	−0.867797	+	0.501023i	−0.00118172	+	0.999999i	$0.500376\pi$
$758$	−3.14402	−	2.26690i	−0.114196	−	0.0823377i
$759$			1.64069i			0.0595531i
$760$	−11.3921	−	12.3789i	−0.413234	−	0.449030i
$761$	32.0510	+	18.5047i	1.16185	+	0.670794i	0.951746	−	0.306885i	$-0.0992869\pi$
$761$	32.0510	+	18.5047i	1.16185	+	0.670794i	0.210103	+	0.977679i	$0.432620\pi$
$762$	−14.9523	−	1.51680i	−0.541666	−	0.0549480i
$763$	32.6419	+	18.8458i	1.18172	+	0.682265i
$764$	−1.72144	−	5.17026i	−0.0622794	−	0.187053i
$765$	−0.759841	−	1.31608i	−0.0274721	−	0.0475831i
$766$	42.6207	+	4.32355i	1.53995	+	0.156216i
$767$	−19.0618	−	12.3498i	−0.688280	−	0.445925i
$768$	−14.1571	+	13.5102i	−0.510850	+	0.487508i
$769$	−31.5869	+	18.2367i	−1.13905	+	0.657632i	−0.946196	−	0.323595i	$-0.895108\pi$
$769$	−31.5869	+	18.2367i	−1.13905	+	0.657632i	−0.192856	+	0.981227i	$0.561775\pi$
$770$	3.01913	+	6.71550i	0.108802	+	0.242010i
$771$	−0.152834	−	0.0882390i	−0.00550420	−	0.00317785i
$772$	1.80194	−	8.79020i	0.0648533	−	0.316366i
$773$	−21.9341	+	37.9909i	−0.788914	+	1.36644i	0.137719	+	0.990471i	$0.456023\pi$
$773$	−21.9341	+	37.9909i	−0.788914	+	1.36644i	−0.926633	+	0.375968i	$0.877310\pi$
$774$	1.69002	−	2.34393i	0.0607467	−	0.0842508i
$775$		−	0.814108i		−	0.0292436i
$776$	10.4910	−	9.65470i	0.376606	−	0.346584i
$777$	−22.1003	−	38.2788i	−0.792843	−	1.37324i
$778$	1.66818	+	3.71056i	0.0598072	+	0.133030i
$779$		−	52.4382i		−	1.87879i
$780$	8.53784	+	2.21175i	0.305704	+	0.0791933i
$781$			6.66129i			0.238360i
$782$	−1.52784	+	0.686882i	−0.0546355	+	0.0245628i
$783$	−9.68874	−	16.7814i	−0.346247	−	0.599718i
$784$	43.8746	−	32.8587i	1.56695	−	1.17352i
$785$		−	8.00548i		−	0.285728i
$786$	−25.9731	−	18.7271i	−0.926428	−	0.667975i
$787$	7.49466	−	12.9811i	0.267156	−	0.462727i	−0.700971	−	0.713190i	$-0.747250\pi$
$787$	7.49466	−	12.9811i	0.267156	−	0.462727i	0.968126	+	0.250463i	$0.0805829\pi$
$788$	−43.6504	−	8.94809i	−1.55498	−	0.318762i
$789$	−26.9560	−	15.5630i	−0.959659	−	0.554059i
$790$	7.22545	−	3.24840i	0.257070	−	0.115573i
$791$	43.0248	−	24.8404i	1.52978	−	0.883222i
$792$	1.45384	−	4.64566i	0.0516598	−	0.165076i
$793$	23.8755	−	36.8516i	0.847844	−	1.30864i
$794$	−0.560774	+	5.52800i	−0.0199011	+	0.196181i
$795$	−4.95360	−	8.57989i	−0.175686	−	0.304297i
$796$	−14.8029	−	44.4598i	−0.524674	−	1.57584i
$797$	−34.9581	−	20.1831i	−1.23828	−	0.714921i	−0.269538	−	0.962990i	$-0.586871\pi$
$797$	−34.9581	−	20.1831i	−1.23828	−	0.714921i	−0.968742	+	0.248069i	$0.920204\pi$
$798$	−4.72441	+	46.5723i	−0.167242	+	1.64864i
$799$	−7.92514	−	4.57558i	−0.280371	−	0.161872i
$800$	−2.91670	−	4.84694i	−0.103121	−	0.171365i
$801$		−	21.0338i		−	0.743192i
$802$	11.7481	−	16.2937i	0.414840	−	0.575351i
$803$	14.4468	−	8.34086i	0.509817	−	0.294343i
$804$	24.2819	−	8.08465i	0.856356	−	0.285124i
$805$			5.33441i			0.188013i
$806$	−3.86840	+	1.50582i	−0.136259	+	0.0530403i
$807$	27.5033			0.968163
$808$	−4.96340	−	22.1636i	−0.174612	−	0.779714i
$809$	8.95469	+	15.5100i	0.314830	+	0.545302i	0.979401	−	0.201923i	$-0.0647191\pi$
$809$	8.95469	+	15.5100i	0.314830	+	0.545302i	−0.664571	+	0.747225i	$0.731386\pi$
$810$	−2.55276	−	1.84060i	−0.0896949	−	0.0646720i
$811$	4.16655			0.146307			0.0731536	−	0.997321i	$-0.476694\pi$
$811$	4.16655			0.146307			0.0731536	+	0.997321i	$0.476694\pi$
$812$	−21.2463	+	23.9430i	−0.745598	+	0.840235i
$813$	7.64246	−	13.2371i	0.268033	−	0.464246i
$814$	−1.29711	+	12.7867i	−0.0454637	+	0.448172i
$815$	1.57351	−	2.72541i	0.0551178	−	0.0954668i
$816$	−4.90785	+	0.587863i	−0.171809	+	0.0205793i
$817$	6.99756	−	4.04004i	0.244813	−	0.141343i
$818$	2.41477	+	0.244961i	0.0844306	+	0.00856485i
$819$	11.2262	+	21.9744i	0.392277	+	0.767848i
$820$	3.54096	−	17.2734i	0.123656	−	0.603214i
$821$	−0.647798	−	1.12202i	−0.0226083	−	0.0391587i	0.854500	−	0.519452i	$-0.173864\pi$
$821$	−0.647798	−	1.12202i	−0.0226083	−	0.0391587i	−0.877108	+	0.480293i	$0.840530\pi$
$822$	−2.59058	+	1.16466i	−0.0903568	+	0.0406223i
$823$	15.5669	−	26.9626i	0.542628	−	0.939859i	−0.456124	−	0.889916i	$-0.650763\pi$
$823$	15.5669	−	26.9626i	0.542628	−	0.939859i	0.998752	−	0.0499428i	$-0.0159039\pi$
$824$	5.15086	−	16.4593i	0.179439	−	0.573388i
$825$	−1.21198	−	0.699734i	−0.0421956	−	0.0243616i
$826$	23.7073	−	32.8801i	0.824882	−	1.14405i
$827$	5.94622			0.206770			0.103385	−	0.994641i	$-0.467033\pi$
$827$	5.94622			0.206770			0.103385	+	0.994641i	$0.467033\pi$
$828$	2.34078	−	2.63789i	0.0813477	−	0.0916731i
$829$	39.5944	−	22.8599i	1.37517	−	0.793956i	0.383598	−	0.923500i	$-0.374685\pi$
$829$	39.5944	−	22.8599i	1.37517	−	0.793956i	0.991574	+	0.129544i	$0.0413514\pi$
$830$	−2.98796	+	1.34332i	−0.103714	+	0.0466273i
$831$	17.7632			0.616200
$832$	−17.6363	+	22.8245i	−0.611430	+	0.791298i
$833$	13.8457			0.479723
$834$	−26.6287	+	11.9716i	−0.922076	+	0.414544i
$835$	−9.82233	+	5.67093i	−0.339916	+	0.196250i
$836$	9.03428	−	10.1810i	0.312457	−	0.352117i
$837$	4.48478			0.155017
$838$	6.94648	−	9.63422i	0.239962	−	0.332809i
$839$	−1.47495	−	0.851562i	−0.0509209	−	0.0293992i	0.474323	−	0.880351i	$-0.342693\pi$
$839$	−1.47495	−	0.851562i	−0.0509209	−	0.0293992i	−0.525244	+	0.850951i	$0.676026\pi$
$840$	−4.70110	+	15.0221i	−0.162203	+	0.518313i
$841$	−8.31348	+	14.3994i	−0.286672	+	0.496530i
$842$	9.56735	−	4.30126i	0.329713	−	0.148231i
$843$	−5.90893	−	10.2346i	−0.203514	−	0.352497i
$844$	4.97343	−	24.2613i	0.171192	−	0.835107i
$845$	12.9317	+	1.33112i	0.444863	+	0.0457919i
$846$	19.1678	+	1.94443i	0.659002	+	0.0668508i
$847$	38.1867	−	22.0471i	1.31211	−	0.757547i
$848$	32.1712	−	3.85347i	1.10476	−	0.132329i
$849$	9.12254	−	15.8007i	0.313085	−	0.542279i
$850$	0.144207	−	1.42156i	0.00494626	−	0.0487592i
$851$	−4.65570	+	8.06391i	−0.159595	+	0.276427i
$852$	−9.45184	+	10.6515i	−0.323815	+	0.364916i
$853$	−20.2265			−0.692544			−0.346272	−	0.938134i	$-0.612552\pi$
$853$	−20.2265			−0.692544			−0.346272	+	0.938134i	$0.612552\pi$
$854$	63.5662	+	45.8326i	2.17519	+	1.56836i
$855$	4.47310	+	7.74764i	0.152977	+	0.264964i
$856$	6.20269	+	27.6975i	0.212004	+	0.946683i
$857$	−26.9722			−0.921354			−0.460677	−	0.887568i	$-0.652393\pi$
$857$	−26.9722			−0.921354			−0.460677	+	0.887568i	$0.652393\pi$
$858$	−1.08319	+	7.05323i	−0.0369796	+	0.240793i
$859$			5.18933i			0.177058i	0.996074	+	0.0885288i	$0.0282165\pi$
$859$			5.18933i			0.177058i	−0.996074	+	0.0885288i	$0.971783\pi$
$860$	2.57784	−	0.858292i	0.0879037	−	0.0292675i
$861$	−42.4905	+	24.5319i	−1.44807	+	0.836046i
$862$	−24.8897	+	34.5200i	−0.847746	+	1.17576i
$863$			14.0474i			0.478179i	0.970998	+	0.239089i	$0.0768489\pi$
$863$			14.0474i			0.478179i	−0.970998	+	0.239089i	$0.923151\pi$
$864$	26.7010	−	16.0676i	0.908385	−	0.546632i
$865$	−17.0348	−	9.83505i	−0.579201	−	0.334402i
$866$	−5.88210	+	57.9845i	−0.199882	+	1.97039i
$867$	16.9253	+	9.77181i	0.574812	+	0.331868i
$868$	−2.34038	−	7.02922i	−0.0794377	−	0.238587i
$869$	3.20484	+	5.55095i	0.108717	+	0.188303i
$870$	0.614046	−	6.05314i	0.0208181	−	0.205221i
$871$	33.5927	−	17.1618i	1.13825	−	0.581505i
$872$	6.99754	−	22.3603i	0.236967	−	0.757216i
$873$	−6.56608	+	3.79093i	−0.222228	+	0.128303i
$874$	8.99423	−	4.04360i	0.304235	−	0.136777i
$875$	−3.94053	−	2.27507i	−0.133214	−	0.0769113i
$876$	34.9358	+	7.16165i	1.18037	+	0.241970i
$877$	−15.2443	+	26.4039i	−0.514764	+	0.891598i	0.485089	+	0.874465i	$0.338787\pi$
$877$	−15.2443	+	26.4039i	−0.514764	+	0.891598i	−0.999853	+	0.0171330i	$0.994546\pi$
$878$	38.8693	+	28.0256i	1.31178	+	0.945819i
$879$		−	1.07489i		−	0.0362551i
$880$	3.66342	−	2.74362i	0.123494	−	0.0924874i
$881$	−13.6820	−	23.6980i	−0.460959	−	0.798404i	0.538050	−	0.842913i	$-0.319161\pi$
$881$	−13.6820	−	23.6980i	−0.460959	−	0.798404i	−0.999009	+	0.0445085i	$0.985828\pi$
$882$	−26.5863	+	11.9526i	−0.895208	+	0.402465i
$883$		−	15.1443i		−	0.509647i	−0.966988	−	0.254824i	$-0.917983\pi$
$883$		−	15.1443i		−	0.509647i	0.966988	−	0.254824i	$-0.0820174\pi$
$884$	−7.02159	+	1.94418i	−0.236162	+	0.0653898i
$885$			7.70457i			0.258986i
$886$	−21.0248	−	46.7657i	−0.706341	−	1.57112i
$887$	−0.725904	−	1.25730i	−0.0243735	−	0.0422161i	0.853581	−	0.520960i	$-0.174426\pi$
$887$	−0.725904	−	1.25730i	−0.0243735	−	0.0422161i	−0.877955	+	0.478743i	$0.841092\pi$
$888$	−20.2174	+	18.6057i	−0.678451	+	0.624365i
$889$		−	39.5359i		−	1.32599i
$890$	11.5664	−	16.0417i	0.387707	−	0.537719i
$891$	1.27316	−	2.20517i	0.0426523	−	0.0738760i
$892$	−9.04647	+	44.1303i	−0.302898	+	1.47759i
$893$	46.6545	+	26.9360i	1.56123	+	0.901378i
$894$	10.4902	+	23.3336i	0.350846	+	0.780391i
$895$	−2.69851	+	1.55798i	−0.0902012	+	0.0520777i
$896$	−39.1175	−	33.4649i	−1.30682	−	1.11798i
$897$	−2.81109	+	4.33889i	−0.0938596	+	0.144871i
$898$	2.59756	+	0.263503i	0.0866818	+	0.00879322i
$899$	1.43183	+	2.47999i	0.0477540	+	0.0827124i
$900$	0.950295	+	2.85417i	0.0316765	+	0.0951389i
$901$	7.08770	+	4.09209i	0.236126	+	0.136327i
$902$	14.1936	+	1.43983i	0.472594	+	0.0479411i
$903$	−6.54727	−	3.78007i	−0.217880	−	0.125793i
$904$	−20.9125	−	22.7240i	−0.695538	−	0.755789i
$905$			24.7399i			0.822384i
$906$	10.1666	+	7.33034i	0.337763	+	0.243534i
$907$	−37.6451	+	21.7344i	−1.24999	+	0.721680i	−0.971106	−	0.238647i	$-0.923296\pi$
$907$	−37.6451	+	21.7344i	−1.24999	+	0.721680i	−0.278879	+	0.960326i	$0.589963\pi$
$908$	10.2795	+	30.8741i	0.341138	+	1.02459i
$909$			12.0781i			0.400607i
$910$	−3.52182	+	22.9324i	−0.116747	+	0.760201i
$911$	−13.1889			−0.436969			−0.218485	−	0.975840i	$-0.570111\pi$
$911$	−13.1889			−0.436969			−0.218485	+	0.975840i	$0.570111\pi$
$912$	28.8920	−	3.46069i	0.956710	−	0.114595i
$913$	−1.32531	−	2.29550i	−0.0438613	−	0.0759699i
$914$	−2.91452	+	4.04221i	−0.0964038	+	0.133705i
$915$	−14.8950			−0.492414
$916$	7.83641	−	8.83107i	0.258922	−	0.291787i
$917$	42.1168	−	72.9484i	1.39082	−	2.40897i
$918$	7.83115	+	0.794411i	0.258466	+	0.0262195i
$919$	0.465901	−	0.806964i	0.0153687	−	0.0266193i	−0.858239	−	0.513251i	$-0.828441\pi$
$919$	0.465901	−	0.806964i	0.0153687	−	0.0266193i	0.873607	+	0.486631i	$0.161774\pi$
$920$	3.23580	−	0.724636i	0.106681	−	0.0238906i
$921$	−20.0902	+	11.5991i	−0.661994	+	0.382203i
$922$	−5.39196	+	53.1528i	−0.177575	+	1.75050i
$923$	−11.4132	+	17.6162i	−0.375670	+	0.579843i
$924$	−12.4761	−	2.55753i	−0.410434	−	0.0841366i
$925$	−3.97121	−	6.87834i	−0.130573	−	0.226158i
$926$	−0.0310156	−	0.0689885i	−0.00101924	−	0.00226710i
$927$	−4.58568	+	7.94262i	−0.150613	+	0.260870i
$928$	17.4097	+	9.63530i	0.571502	+	0.316294i
$929$	−3.92370	−	2.26535i	−0.128732	−	0.0743236i	0.434251	−	0.900792i	$-0.357013\pi$
$929$	−3.92370	−	2.26535i	−0.128732	−	0.0743236i	−0.562983	+	0.826468i	$0.690346\pi$
$930$	1.14220	+	0.823554i	0.0374544	+	0.0270054i
$931$	−81.5079			−2.67131
$932$	−0.273186	+	0.307861i	−0.00894852	+	0.0100843i
$933$	7.86858	−	4.54293i	0.257606	−	0.148729i
$934$	−1.01094	−	2.24865i	−0.0330790	−	0.0735781i
$935$	1.15608			0.0378078
$936$	11.8045	−	9.79476i	0.385841	−	0.320152i
$937$	44.1517			1.44237			0.721186	−	0.692741i	$-0.243597\pi$
$937$	44.1517			1.44237			0.721186	+	0.692741i	$0.243597\pi$
$938$	27.6058	+	61.4039i	0.901361	+	2.00491i
$939$	19.4647	−	11.2380i	0.635208	−	0.366737i
$940$	13.5493	+	12.0233i	0.441931	+	0.392155i
$941$	35.8738			1.16945			0.584726	−	0.811231i	$-0.301202\pi$
$941$	35.8738			1.16945			0.584726	+	0.811231i	$0.301202\pi$
$942$	11.2318	+	8.09837i	0.365952	+	0.263859i
$943$	8.95117	+	5.16796i	0.291490	+	0.168292i
$944$	−23.1652	−	9.91409i	−0.753962	−	0.322676i
$945$	12.5330	−	21.7077i	0.407697	−	0.706152i
$946$	0.901390	+	2.00497i	0.0293067	+	0.0651873i
$947$	8.27885	+	14.3394i	0.269026	+	0.465967i	0.968611	−	0.248583i	$-0.0799648\pi$
$947$	8.27885	+	14.3394i	0.269026	+	0.465967i	−0.699584	+	0.714550i	$0.746631\pi$
$948$	−2.75174	+	13.4235i	−0.0893725	+	0.435975i
$949$	52.4963	+	2.69473i	1.70410	+	0.0874747i
$950$	−0.848931	+	8.36860i	−0.0275430	+	0.271513i
$951$	−9.67001	+	5.58298i	−0.313572	+	0.181041i
$952$	−2.84156	−	12.6887i	−0.0920955	−	0.411244i
$953$	−22.7172	+	39.3473i	−0.735881	+	1.27458i	0.218454	+	0.975847i	$0.429899\pi$
$953$	−22.7172	+	39.3473i	−0.735881	+	1.27458i	−0.954336	+	0.298737i	$0.903435\pi$
$954$	−17.1424	−	1.73896i	−0.555004	−	0.0563010i
$955$	−1.36233	+	2.35962i	−0.0440838	+	0.0763554i
$956$	−33.4280	−	29.6629i	−1.08114	−	0.959368i
$957$	4.92268			0.159128
$958$	−33.9046	+	47.0230i	−1.09541	+	1.51924i
$959$	−3.73593	−	6.47083i	−0.120640	−	0.208954i
$960$	9.75087	+	0.811003i	0.314708	+	0.0261750i
$961$	30.3372			0.978620
$962$	−25.3385	+	31.5926i	−0.816945	+	1.01859i
$963$		−	15.0939i		−	0.486393i
$964$	−11.4317	+	3.80620i	−0.368192	+	0.122589i
$965$	−3.88542	+	2.24325i	−0.125076	+	0.0722127i
$966$	−7.48426	−	5.39631i	−0.240802	−	0.173623i
$967$		−	59.6969i		−	1.91972i	−0.280473	−	0.959862i	$-0.590491\pi$
$967$		−	59.6969i		−	1.91972i	0.280473	−	0.959862i	$-0.409509\pi$
$968$	−18.5609	−	20.1687i	−0.596569	−	0.648247i
$969$	6.36526	+	3.67499i	0.204482	+	0.118058i
$970$	−7.09233	−	0.719464i	−0.227721	−	0.0231006i
$971$	35.6708	+	20.5945i	1.14473	+	0.660910i	0.947597	−	0.319467i	$-0.103504\pi$
$971$	35.6708	+	20.5945i	1.14473	+	0.660910i	0.197132	+	0.980377i	$0.436837\pi$
$972$	−26.1956	+	8.72183i	−0.840225	+	0.279753i
$973$	−38.4019	−	66.5140i	−1.23111	−	2.13234i
$974$	15.9690	+	1.61994i	0.511680	+	0.0519062i
$975$	−2.00624	−	3.92704i	−0.0642510	−	0.125766i
$976$	19.1666	−	44.7846i	0.613509	−	1.43352i
$977$	8.75025	−	5.05196i	0.279945	−	0.161627i	−0.353453	−	0.935452i	$-0.614993\pi$
$977$	8.75025	−	5.05196i	0.279945	−	0.161627i	0.633399	+	0.773826i	$0.281659\pi$
$978$	2.23201	+	4.96469i	0.0713719	+	0.158753i
$979$	13.8574	+	8.00059i	0.442885	+	0.255700i
$980$	−26.8491	−	5.50393i	−0.857664	−	0.175816i
$981$	−6.22973	+	10.7902i	−0.198900	+	0.344505i
$982$	−3.79231	+	5.25964i	−0.121018	+	0.167842i
$983$		−	36.3609i		−	1.15973i	−0.814712	−	0.579866i	$-0.803105\pi$
$983$		−	36.3609i		−	1.15973i	0.814712	−	0.579866i	$-0.196895\pi$
$984$	20.6528	+	22.4419i	0.658387	+	0.715420i
$985$	11.1395	+	19.2942i	0.354935	+	0.614765i
$986$	2.06090	+	4.58410i	0.0656326	+	0.145987i
$987$		−	50.4054i		−	1.60442i
$988$	41.3354	−	11.4452i	1.31505	−	0.364120i
$989$			1.59264i			0.0506430i
$990$	−2.21989	+	0.998012i	−0.0705528	+	0.0317189i
$991$	−22.6507	−	39.2322i	−0.719523	−	1.24625i	−0.961189	−	0.275891i	$-0.911027\pi$
$991$	−22.6507	−	39.2322i	−0.719523	−	1.24625i	0.241666	−	0.970360i	$-0.422306\pi$
$992$	−3.94593	+	2.37451i	−0.125283	+	0.0753908i
$993$		−	1.61480i		−	0.0512440i
$994$	−30.3866	−	21.9094i	−0.963803	−	0.694923i
$995$	−11.7148	+	20.2907i	−0.371385	+	0.643258i
$996$	1.13794	−	5.55106i	0.0360569	−	0.175892i
$997$	−9.30515	−	5.37233i	−0.294697	−	0.170144i	0.345361	−	0.938470i	$-0.387756\pi$
$997$	−9.30515	−	5.37233i	−0.294697	−	0.170144i	−0.640058	+	0.768326i	$0.721090\pi$
$998$	−34.5953	+	15.5533i	−1.09510	+	0.492330i
$999$	37.8916	−	21.8767i	1.19884	−	0.692148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.a.101.26	✓	56
8.5	even	2		520.2.ca.b.101.21	yes	56
13.4	even	6		520.2.ca.b.381.21	yes	56
104.69	even	6	inner	520.2.ca.a.381.26	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.26	✓	56	1.1	even	1	trivial
520.2.ca.a.381.26	yes	56	104.69	even	6	inner
520.2.ca.b.101.21	yes	56	8.5	even	2
520.2.ca.b.381.21	yes	56	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28986 - 0.579890i) q^{2} +(1.05921 - 0.611534i) q^{3} +(1.32746 - 1.49595i) q^{4} -1.00000 q^{5} +(1.01160 - 1.40301i) q^{6} +(3.94053 + 2.27507i) q^{7} +(0.844743 - 2.69934i) q^{8} +(-0.752053 + 1.30259i) q^{9} +(-1.28986 + 0.579890i) q^{10} +(-0.572114 - 0.990930i) q^{11} +(0.491229 - 2.39630i) q^{12} +(0.184836 - 3.60081i) q^{13} +(6.40201 + 0.649436i) q^{14} +(-1.05921 + 0.611534i) q^{15} +(-0.475720 - 3.97161i) q^{16} +(0.505178 - 0.874994i) q^{17} +(-0.214679 + 2.11626i) q^{18} +(-2.97393 + 5.15100i) q^{19} +(-1.32746 + 1.49595i) q^{20} +5.56512 q^{21} +(-1.31257 - 0.946395i) q^{22} +(-0.586182 - 1.01530i) q^{23} +(-0.755977 - 3.37575i) q^{24} +1.00000 q^{25} +(-1.84966 - 4.75171i) q^{26} +5.50883i q^{27} +(8.63427 - 2.87478i) q^{28} +(-3.04627 + 1.75877i) q^{29} +(-1.01160 + 1.40301i) q^{30} -0.814108i q^{31} +(-2.91670 - 4.84694i) q^{32} +(-1.21198 - 0.699734i) q^{33} +(0.144207 - 1.42156i) q^{34} +(-3.94053 - 2.27507i) q^{35} +(0.950295 + 2.85417i) q^{36} +(-3.97121 - 6.87834i) q^{37} +(-0.848931 + 8.36860i) q^{38} +(-2.00624 - 3.92704i) q^{39} +(-0.844743 + 2.69934i) q^{40} +(-7.63515 + 4.40815i) q^{41} +(7.17821 - 3.22716i) q^{42} +(-1.17648 - 0.679243i) q^{43} +(-2.24184 - 0.459564i) q^{44} +(0.752053 - 1.30259i) q^{45} +(-1.34485 - 0.969666i) q^{46} -9.05737i q^{47} +(-2.93266 - 3.91584i) q^{48} +(6.85187 + 11.8678i) q^{49} +(1.28986 - 0.579890i) q^{50} -1.23573i q^{51} +(-5.14126 - 5.05642i) q^{52} +8.10029i q^{53} +(3.19451 + 7.10559i) q^{54} +(0.572114 + 0.990930i) q^{55} +(9.46991 - 8.71497i) q^{56} +7.27464i q^{57} +(-2.90936 + 4.03506i) q^{58} +(3.14969 - 5.45542i) q^{59} +(-0.491229 + 2.39630i) q^{60} +(10.5468 + 6.08920i) q^{61} +(-0.472093 - 1.05008i) q^{62} +(-5.92698 + 3.42194i) q^{63} +(-6.57282 - 4.56049i) q^{64} +(-0.184836 + 3.60081i) q^{65} +(-1.96904 - 0.199745i) q^{66} +(5.23119 + 9.06069i) q^{67} +(-0.638344 - 1.91724i) q^{68} +(-1.24178 - 0.716940i) q^{69} +(-6.40201 - 0.649436i) q^{70} +(-5.04169 - 2.91082i) q^{71} +(2.88084 + 3.13040i) q^{72} +14.5790i q^{73} +(-9.11096 - 6.56920i) q^{74} +(1.05921 - 0.611534i) q^{75} +(3.75786 + 11.2866i) q^{76} -5.20639i q^{77} +(-4.86501 - 3.90192i) q^{78} -5.60175 q^{79} +(0.475720 + 3.97161i) q^{80} +(1.11268 + 1.92721i) q^{81} +(-7.29200 + 10.1134i) q^{82} +2.31651 q^{83} +(7.38746 - 8.32514i) q^{84} +(-0.505178 + 0.874994i) q^{85} +(-1.91138 - 0.193895i) q^{86} +(-2.15109 + 3.72580i) q^{87} +(-3.15814 + 0.707246i) q^{88} +(-12.1107 + 6.99213i) q^{89} +(0.214679 - 2.11626i) q^{90} +(8.92044 - 13.7686i) q^{91} +(-2.29696 - 0.470865i) q^{92} +(-0.497854 - 0.862309i) q^{93} +(-5.25227 - 11.6827i) q^{94} +(2.97393 - 5.15100i) q^{95} +(-6.05347 - 3.35025i) q^{96} +(4.36544 + 2.52039i) q^{97} +(15.7199 + 11.3344i) q^{98} +1.72104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30}+ \cdots + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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